SlideShare a Scribd company logo
กกกกกกกกกกกกกกกกกก
สสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
สสสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
กกกกกกกกกกก
หหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหหหหหหหหหหหหหหหหหหหหหห
สสสสสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
สสสสสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
สสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหห) หหหหหหห(หหหห) หหหหหหห(หหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหห
หหหหหหห หหหหหหห หหหห
หหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหห
หหหหหหห หหหหหหหหหหห (หหห
250
C)
หหหหหหหหหหห
( 0
C )
หหหหหหหห
( 0
C )
หหหหหหห
หหหหหหหห
หหหห
หหหหหห
หหหหหหห
หหหหหหหห
หหหหหหห
หหหหหหห
หหหหหหห
หหหหหหห
หหหห
หหหห
97.8
838
-38.4
-7.2
-269.7
-210
892
1440
357
58
-268.9
-195.8
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห97.8 0
C หหหหหหหหหห892 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหห97.8 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห97.8 - 892 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
892 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหห25 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห2 หหหหหหหหหหหหหหหหหหหห25 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห25 0
C หหหหหหหหหหหหหหหหหหหห250
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห25 0
C
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(CH3COOH) หหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหห117.9 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห16.6 - 117.9 0
C
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห16.6 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห10 mmHg หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห50 0
C หหหหหหห
กกกกกกกกกกกกก
กกกกกกกกกกกกกกกกกกกกกกกกกกกก
1.กกกกกกกกกกกกกกกกกกกกกกกกกกกกกกกกหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห10 หหหหหหหหหหหหหหหหหหหหหหหหห10 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
2.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Random Motion) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
3.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
4.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
5.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหF2 (หหหหหหหหหหหห) , Cl2 (หหหหหหหหหหหหหห) , Br2 (หหหหห) , I2 (หหหหหหหหห) , NO2
(หหหหหหหหหหหห) , SO2 (หหหหหหหหหหหหหหหหห) หหหH2S (หหหหหหหหหหหหหหหหหห) หหหหหหห
2
6.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 หหหหหหหหห22.4 หหหหหหห0 0
C , 1 atm หหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหT (หหหหหห) หหหt (หหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห100 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหห
สสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสส
1.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(0
C) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห100 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 0
C
2.หหหหหหหหหหหหหหหห(0
F) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห180 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 0
F
3.หหหหหหหหหหห(K) หหหหหหหหหหหหหหหหหหหหหหหหห(Absolute Temperature) หหหหหหหหหSI หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห100 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1
K
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหห= 0 0
C = 273.15K = 32 0
F
หหหหหหหหหหหหหหห= 100 0
C= 373.15 K = 212 0
F
375.15
273.15
0
(K)
100
0
-273.15
212
-32
-459.7
(0C) (0F)
หหหหหห หหหหหหหห หหหหหหหหหหห
หหหหหห4.2 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหห3 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
T = 273.15 + t
T = 273.15 + 9
5
( F - 32 )
t = 9
5
( F - 32 )
3
หหหหหT = หหหหหหหหหหหหหห
t = หหหหหหหหหหหหหหหห
F = หหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
T = 273.15 + t
T = 273.15 + 9
5
( F - 32 )
t = 9
5
( F - 32 )
หหหหหหหหหหหหหหหหหหหหหหหP หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Barometer) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 cm2
หหหหหหหหห100 cm หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 cm3
หหหหหหหหหหหหหหหหหหหหหหหหห76 cm หหหห760 mm หหหหหหหหหหหห1 หหหหหหหห(atm)
หหหหหห4.3 หหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหห)
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Nanometer)หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหห)
4
หหหหหหหหหหหหหหหหหหห(หหหห. ) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(h) (หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห)
หหหหหหหหหหหหหหหหหหหหหหห2 หหหห(หหหห. ) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห2 หหหห(h) หหหหหหหหหหหหหหหหหหหหหหหห
กกกกกกกกกกกกกกกกกกกกกกกกกกกกกก
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหห) หหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหh หหหหหหหหห(หหหหห4.3 หหหหหห)
หหห
หหห(F) = หหหหหหห(m) x หหหหหหหหหหหหหหห(g)
หหหหหหหหหห= หหหหหหหหหหห(V) x หหหหหหหหหหหหหหห(d)
หหหหหหหหหหห
F = mg = Vdg
= (Ah)dg หหหหหA = หหหหหหหหหหหหหหหหหหหหห
หหหหหหหหห
หหหหหหห(P) = (A)หหหหหหห
(F)หหห
หหหหหหหหหหห P = dgA
Ah
= hdg
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห25 0
C หหหหหหหหหหหห76.1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
P = hdg = (76.1 cm) x (13.596
g/cm3
) x (980.7 cm/s2
)
= 1.015 x 106
g/cm.s2
= 1.015 x 106
dyne/cm2
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห76 หหหหหหหหหหหห0 0
C หหหหหหหหหหหหห1 หหหหหหหห( 1 atm)
หหหหหหหหหหหหหห( 1 atm) หหหหหหหหหdyne/cm2
หหหหหหหหหหหห
P (1 atm) = hdg
= (76.0 cm) x (13.596 g/cm3
)
x (980.7 cm/s2
)
= 1.013 x 106
dyne cm-2
5
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหatm หหหหdyne cm-2
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห( N/cm2
) , หหหหหหหหหหหหหหหหหห(N/m2
) หหหหหหหหหหหหหหหหหหหหหหห
S.I. ( 1 Pa = 1 kg/m. s2
), หหหหหหหหหหหหหหหหห(pound per square
inches) หหหหp.s.i ) , mm Hg หหหหtorr หหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหatm หหหmm Hg หหหPa หหหหหหหหหหหหหหหหหหหหหหหหหหห
1 atm = 760 mm Hg = 76 cm
Hg
= 760 torr = 17.7
p.s.i
= 1.013 x 105
Pa = 1.013 x 105
N/m2
= 1.013 x 106
dyne cm-2
กกกกกกกกกกกกกกกกกกกกกกกกก
หหหหหหหหหหหหหหหหSTP หหหหหหหหหหหหStandard Temperature and Pressure หหหห
NTP หหหหหหหหหหหหNormal Temperature and Pressure หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหห00
C หหหห273.15 K (273 K หหหหหหหหห)
หหหหหหหหหหหหหหหหหหหหหหหห1 atm หหหห760 mm Hg
กกกกกกกกกกกกกก
หหหหหหหหหหหหหหหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(V) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห( หหห) หหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหdm3
หหหcm3
หหหหหหหหหหหหหS.I หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
1 หหหห = 1000.027 cm3
= 1 dm3
(หหหหหหหหห)
1 หหหหหหหหห= 1.000027 cm3
= 1 cm3
(หหหหหหหหห)
หหหหหหหหหหห1 dm3
= 103
cm3
= 1 หหหห= 103
หหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
กกกกกกกกกกกกก
6
หหหหหหหหหหหหหหหหหหหหหหหหหหหหห2 หหหหหหหหหหหห
ส. สสสสสสสสสสส( ideal gas) หหหหหหหหหหหหหหห(perfect gas) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
ส. สสสสสสสส(real gas) สสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 , O2 CO2 , หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
1 กกกกกกกกกกกกกก
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
ก. กกกกกกกกกก(Boyle ,
s Law)
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห.ห. 1662 (ห.ห. 2205) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Robert Boyle) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
“ หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห”
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
V α P
1
หหหหหหหหหหหหหหหหหหหหหหหห
หหห V = P
k
หหหหPV = k
หหหหหV = หหหหหหหหหหหหหห
P = หหหหหหหหหหหหหห
k = หหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหห
P1V1 = P2V2 = P3V3 = ……..
หหหk หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหk หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหk หหหหหหหหหหหหหหหหหหหหหk หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP , V หหหหหหหหห
หหหหหหหหPV = k หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห“ หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห” หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหห
7
หหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหห
หหหหหห1 หหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Hyperbolar)
หหห V = P
k
หหหหหP = 0 หหห V = ∞
V = 0 หหห P = ∞
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหหหหหV
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Isotherm) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Isothermal Process)
หหหหหห4.6 หหหหหหหหหหหหหหหหหหหP หหหV หหหหหT หหหn หหหหห
หหหหหห2 หหหหหหหหหหหหหหหหหหหหหP หหหV
1
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Origin) หหหหหหหหหหหหหหหหห
V = P
k
= k P
1
+ 0 หหหหP = k V
1
+ 0
8
หหหหหหหหหหหหหหหหหหหหหหหหหหหy = ax + b หหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV
1
หหหหV หหหP
1
หหหหหหหหหหหหหหหหหหหหหหหหหหหห(Slope = k หหหหหหหหหหห
(Intercept) = 0 หหหหหหหหหหหหหหหหหหหหหหหหหหหหห)
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหห4.7 หหหหหหหหหหหหหหหหหหหP หหหV
1
(หหหหV หหหP
1
)
หหหหหห3 หหหหหหหหหหหหหหหหหหหหหPV หหหP หหหหPV หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหP (หหหหV หหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหห= 0 หหหหหหหหหหหหหหหหหหหหหหหหหหห
PV = k
หหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหPV หหหP (หหหหPV หหหV)
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(P1V1 ≠ P2V2 ) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 , He , N2 ,
CH4 หหหCO2 หหห40 0
C หหหหหหหหหหหหหหหหหหหหห0 - 800 atm หหหหหหหหหหหหหหPV หหหP หหหหหหหหหหห
9
หหหหหหหหหหหหหหหหหหหหหหPV หหหP หหหหหหหหหหห
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหห1 หหหหหหหหหหหหหหหหหหหหหห
หหหหHe
P
(atm
)
V (dm3
) PV (dm3
atm)
-100
0
C
0 0
C 100
0
C
-100
0
C
0 0
C 100
0
C
5
25
50
75
100
2.85
1
0.57
9
0.29
6
0.20
1
0.15
4
4.48
9
0.90
7
0.45
9
0.31
0
0.23
6
6.12
4
1.23
4
0.62
3
0.41
9
0.31
7
14.2
35
14.4
93
14.7
97
15.1
06
15.4
20
22.4
47
22.6
84
22.9
80
23.2
76
23.5
73
30.6
21
30.8
48
31.1
33
31.4
17
31.7
02
10
หหหหH2
5
25
50
75
100
2.84
8
0.57
7
0.29
4
0.19
9
0.15
3
4.49
1
0.91
0
0.46
2
0.31
3
0.23
8
6.13
2
1.23
9
0.62
7
0.42
3
0.32
1
14.2
40
14.4
34
14.7
01
14.9
92
15.3
09
22.4
57
22.7
39
23.0
97
23.4
61
23.8
30
30.6
62
30.9
73
31.3
63
31.7
52
32.1
41
ก. กกกกกกกกกกกก(Charles ,
law)
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหห.ห. 1787 (ห.ห. 2330) หหหหหหหหหหหห(Jacques Charles) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 , หหหหห,
O2 , หหหCO2 หหหหหหหหหหหหหห0 - 80 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
หหหหหหหหหหหหหหห(Joseph Gay - Lussac) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห273.15
1
หหหหหหหหหหหหหหหหห0 0
C
หหหหหหV0 = หหหหหหหหหห0 0
C
V = หหหหหหหหหหt 0
C
หหหหหหหหหหหหหหหหหหหหหหt 0
C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
V = V0 + 273.15
1
V0T = V0( 1 + 273.15
t
)
= V0 273.15
t)(273.15+
หหหหหห T = 273.15 + t
T0 = 273.15
หหหหห V = V0( 0T
T
) หหหห T
V
= 0
0
T
V
หหหหหหหหหหหหหหหหหหหหหหหหหห0
0
T
V
หหหหหหหหหหหหT
V
หหหหหหหหหหหหหหหหห T
V
= k
หหหหหหหV หหหหหหหหหหหT หหหหหหหหT หหหหหหหหหV หหหหหหหหหหหT หหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
“ สสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสส”
หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห
11
V α T (เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ)
เเเเเเเเเเเ V = kT เเเเ T
V
= k
เเเเ 1
1
T
V
= 2
2
T
V
= n
n
T
V
= …….
เเเเเ
k เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเT
T เเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ2 เเเเเเเเเ
เเเเเเ1 เเเเเเเเเเเเเเV เเเT เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV = kT เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ= k
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ“ เเเเเเเเเเเเเเเเ(Isobar)” เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เ. เเเเเเเเเเเเเเเเ( P เเเเเเเเเเ) เ. เเเเเเเเเเเเเเเ(P เเเเเเเ)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเ2 เเเเเเเเเเเเเเเเเเเเเV เเเt (0
C) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
12
เ. เเเเเเเเเเเเเเเเ( P เเเเเเเเเเ) เ. เเเเเเเเเเเเเเเ(P เเเเเเเ)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ2 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ-273.15 0
C เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ-273.15 0
C เเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเ= 273.15 + เเเเเเเเเเเเเเเเ
T = 273.15 + t
เเเเ T = 273 + t
เเเเเเเเT = 273 + t เเเเเเเเเเเเเเเเV = kT เเเเเ
V = kT = k(273 + t )
เเเเเเเเเเเ
V = kt + 273k
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(y = ax + b) เเเเเเเเเเเเเเเเเเเเเV เเเt เเเเเเเเเเเเ= 273k เเเเเเเเเเ= k เเเเเเเเเเเเ)
เเเเเเเเเเเเเเเเเเเV เเเT เเเV เเเt เเเเเเเเเเเเเเเเเเเเเเเเ
13
เเเเเเ4.2 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเ0 เเเเเเเเเเ-273.15 0
C เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเ
ค.คคคคคคคคคคคคคคค(Gay - Lussac ,
s Law)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(Amanton s law) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(P) เเเเเเเเเเเ(T) เเเเเเเเเเเเเเ
“ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ”
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
P α T เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเ P = kT เเเเT
P
= k
เเเ 1T
P1
= 2T
2P
เเเเ 2P
1P
= 2T
1T
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP เเเT เเเเเเเเเเเเHe 1 เเเเเเเเเเเเเ22.4 เเเเ
P
(atm)
0.5 0.6 0.8 1.0 1.2 1.5
14
T(K) 136.5 163.8 218.4 173.0 327.6 409.5
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP เเเT เเเP เเเt เเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเP เเเT เเเP เเเt
ค. คคคคคคคคคคคคคค(Avogadro ,
s law)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
“ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(เเเเเเเเเ) เเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
V α n เเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเV = kn เเเเ n
V
= k
เเเ
1n
1V
= 2n
2V
เเเเ 2V
1V
= 2n
1n
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเn เเเN2 เเเ1 atm 273 K
n (เเเ) 0.1 0.2 0.5 0.8 1.0 2.0
V
(dm3
)
2.24 4.48 11.2 17.92 22.4 44.8
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเn เเเเเเเเเเเ
15
เเเเเเเเเเเเเเเเเเเเเเV เเเn
ค. คคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคค
(Combined gas law : equation state of ideal
gas)
คคคคคคคคคเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V เเเT เเเเเเเเเเเเเ
เเเเเเเเเเเเเ V α P
1
เเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเเ V α T เเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเ V α P
T
เเเเเเเเเเเเเ
เเเเเเเเเเเ V = k P
T
เเเเ T
PV
= k
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
1T
1V1P
= 2T
2V2P
= ……
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , T เเเV เเเเเเเเเเเเเเเเเเเเเเเเเเเP , V เเเเT เเเเเเเเเเเเเเเเเเเเเเเเ(n) เเเเเเเเเเเเ
คคคคคคคคคคคคคคคคคคคคคคค
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ1T
1V1P
= 2T
2V2P
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
16
เเเเเเเเเเเเเเเเเเเเเเเV α P
T
เเเเเเเเเเเเเเเเเ V α n
เเเเเเเเเเเเเเเเ V α P
nT
เเเเ V = P
RnT
เเเเ PV = nRT
เเเเเเเเเเPV = nRT เเเเเเ“ เเเเเเเเเเเเเเเเเเเเเเเ” เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
R เเเเเเเเเเเเเเเเเเเเเเเเเเเ(Universal constant) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
R เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเR เเเเเเเเเเเเเเเเเเเเเP ,
V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเR เเเเเเเเเเเเ
เเเเR = 0.082 atm . l . K-1
. Mol-1
เเเเเเเเเเเเเเเเเเเเเเเเเเO2 , H2 , CO2 , เเเเเเเเเเเเเเ
V เเเเl (เเเเ) , P เเเเatm , T เเเเK , เเเn เเเเmol เเเเเเเเเเเR = 0.082 เเเเเเเ
คคคคคคคคR
เเเR เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
R = nT
PV
เเเเเเเเเเเเเเเเเ1 เเเเเเเเเเเเเเเเ22.414 เเเเเเเSTP ( 00
C , 1 atm)
เเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเR เเเเเเ
R = nT
PV
= K)(273.15)mol.1(
l.)22.414()atm1(
= 0.08205 atm . l . K-1
. Mol-1
(เเเเR = 0.082 atm . l . K-1
. Mol-1
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ)
เเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเR เเเเเเเเเเเเเเเ
R = nT
PV
= K)(273.15)mol.1(
.)cm22414()atm1( 3
= 82.05 atm . cm3
. K-1
. Mol-1
เเเR เเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเ4.6 เเเเเเเเเเเเเเเเเเเเเเเเเเเ( T เเเเเเเเเเ, n เเเเเเเ)
17
P V R
atm
atm
mm.Hg
l
cm3
cm3
0.082 l. atm . K-1
. Mol-1
82.05 cm3
atm . K-1
. Mol-
1
62360 cm3
mm.Hg. K-1
.
Mol-1
R เเเเเเเergs = 8.314 x 107
ergs K-
1
mol-1
R เเเเเเเJoule = 8.314 JK-1
mol-1
R เเเเเเเcalory = 1.987 cal K-1
mol-1
เเเเเเเเ1 J = 107
ergs
1 cal = 4.184 J.
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเR = 0.082 l. atm . K-1
. Mol-1
คคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคค
เเเเเเเเเเเเเเเเเเเเเเเเ
n = M
W
= 2310x6.02
N
เเเเเN = เเเเเเเเเเเเเ
M = เเเเเเเเเเ
W = เเเ
n = เเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเPV = nRT เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(d) เเเ
PV = nRT = M
W
RT
เเเเเเเเเเเ M = P
RT
V
W. = P
RTd
เเเเ d = RT
PM
เเเเเ d = V
W
= เเเเเเเเเเเเเเเเเเ(เเเเเเเเเg/dm3
)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V, T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเเเเเเเเเเเเP , V, T เเเw (เเเเd) เเเเM เเเเเเเเเเเเเเเเเเเเเเเเเM เเเเเเเเd เเเเเเเเเเเเเเเ
18
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เเเ d = RT
PM เเเเเเเเเเเเเเเเเเเเเเเM เเเเเเเเเ
เเเT เเเP เเเเเเเ
เเเเเd1 = 1RT
1P
M เเเ d2 = 2RT
2P
M
1T2P
2T1P
2d
1d
= เเเเ
2P
2T2d
1P
1T1d
=
เเเเเเเเเเเเเเเเเเเเเเเเเเเT เเเP เเเเเเเเเเเเ
P
RT
1d1M = เเเ
P
RT
2d2M =
เเเเเ 2d
1d
1M
1M
=
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(N) เเเเเเเเเเเเเเเเP , V , เเเT เเเเเเเเเเเเเเ
PV = nRT = 2310x6.02
NRT
เเเเ
N = 23
10x6.02RT
PV
คคคคคคคคคคคคคคคคคคคคคคคคคคค
คคคคคคคคคคค1 เเเเN2 เเเเเเ10.0 dm3
เเเ25 0
C เเเเเเเเเเเเเเเเเ0.40 atm
เ. เเเเเเเเเเเเเเเเเเเ2.0 atm เเเเเเเเเเเเเเเเเเเเเ? (เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ)
เ. เเเเเเเเเเเเเเเเเเเเเเเเเเเเ5.0 dm3
เเเเเเเเเเเ25 0
C เเเเเเเเเเเเเเเเเเเเเเเเเเเเเ?
เเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เ. เเเP1V1 = P2V2
P1 = 0.40 atm
P2 = 2.0 atm
V1 = 10.0 dm3
19
V2 = ?
เเเเเเเเเเเเเเเเเ 0.40 x 10.0 = 2.0 x V2
V2 = 2.0 dm3
เ. เเเเเเเเเเเเเเเเเเเเเเเ.
P1 = 0.40 atm
P2 = ? atm
V1 = 10.0 dm3
V2 = 5.0 dm3
เเเเเเเเเเเเเเเเเ 0.40 x 10.0 = 5.0 x P2
P2 = 0.8 atm
คคคคคคคคคคค2 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ30 0
C เเเเเเเเเเเเเ380 mm.Hg เเเเเเเเเ500 cm3
เ. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเcm3
เ. เเเเเเเเเเเเเเเเเเเเเเเเเเ100 cm3
เเเเเเเเเเเเเเเเmm.Hg
เเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ
เ. เเเP1V1 = P2V2
P1 = 380 mm.Hg
P2 = 380 + 380 = 760 mm.Hg
V1 = 500 cm3
V2 = ? cm3
เเเเเเเเเเเเเเเเเ 380 x 500 = 760 x V2
V2 = 250 cm3
เเเเเเเเเเเเเ= 500 - 250 = 250 cm3
เ. เเเเเเเเเเเเ100 cm3
P1 = 380 mm.Hg
P2 = ? mm.Hg
V1 = 500 cm3
V2 = 500 + 100 cm3
เเเเเเเเเเเเเเเเเ 380 x 500 = P2 x 600
20
P2 = 316.7 mm.Hg
เเเเเเเเเเเเเ= 380 - 316.7 = 63.3 mm.Hg
คคคคคคคคคคค3 เเเเHe เเเเเเเเเเเเเเเเเเเเเเเเเเ20 0
C เเเเเเเเเเเเเ400 mmHg. เเเเเเเเเเHe เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ20 dm3
เเเเเเเเเเเเเ150
mmHg. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ?
เเเเเเเ เเเเเเเเเเเเเP1V1 = P2V2
P1 = 400 mm.Hg
P2 = 150 mm.Hg
V1 = ? dm3
V2 = 20 dm3
เเเเเเเเเเเเเเเเเ 400 x V1 = 150 x 20
V1 = 7.5 dm3
เเเเเเเเเเเเเเเเเเเเเเ7.5 เเเเ
คคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคค
คคคคคคคคคคค4. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ200 cm3
เเเ27 0
C เเเเเเเ700 mmHg
เ. เเเเเเเเเเเเเเเเเเเเเ40 0
C เเเเเเเเเเเเเเเเเ(เเเเเเเเเเเเ)
เ. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ120 cm3
เเเ700 mmHg เเเเเเเเเเเเเเเเเเเเเเเเเเ?
เเเเเเเ
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ1
1
T
V
= 2
2
T
V
เ. V1 = 200 cm3
T1 = 273 + 27 = 300 K
V2 = ? cm3
T2 = 273 + 40 = 313 K
เเเเเเเเเเเเเเเเเ
300
200
= 313
V2
V2 = 208.7 cm3
เ. V1 = 200 cm3
21
T1 = 273 + 27 = 300 K
V2 = 120 cm3
T2 = ? K
เเเเเเเเเเเเเเเเเ
300
200
= 2T
120
T2 = 180 K
เเเเเเเเเเเเเเเเเเ180 K เเเเ-93 0
C
คคคคคคคคคคค5 เเเเเเเเเเเเ2.5 เเเเเเเ1 atm 30 0
C
เ. เเเเเเเเเเเเเเเเ10 0
C เเเเเเเเเเเเเเเเเเเเเ
เ. เเเเเเเเเเเเเเเเเเเเเเเเ300 cm3
เเเเเเเเเเเเเเเเเเเ0
C (เเเเเเเเเเเเเเเเเเเเเ2 เเเเเเเเเเเเเเเเเเเเเเ)
เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ1
1
T
V
= 2
2
T
V
เ. เเเเเเเเเเเเเ10 0
C
V1 = 2.5 dm3
T1 = 273 + 30 = 303 K
V2 = ? dm3
T2 = 273 + (30 + 10 ) = 313 K
เเเเเเเเเเเเเเเเเ
303
2.5
= 313
2V
V2 = 2.583 dm3
เ. เเเเเเเเเเเ300 cm3
= 0.300 dm3
V1 = 2.5 dm3
T1 = 273 + 30 = 303 K
V2 = 2.5 - 0.300 dm3
T2 = ? K
เเเเเเเเเเเเเเเเเ
303
2.5
= 2T
2.200
22
T2 = 266.6 K
ตตตตตตตตตตตตตตตตตต266.6 K ตตตตตตตตตตต266.6 - 273 = -6.4 0
C
ตตตตตตตตตตตตตตตตตตตตตตตตตตต30 - (-6.4) = 36.4 0
C
ตตตตตตตตตตต6 ตตตตตตตตตตตตตตตA 5 ตตตตตตตตตตตตตตตตตตตตตตตตตตตต40 0
C ตตตตตตต380 mmHg ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต10 dm3
ตตตตตตตตตตตตตตตตตตตตตตตต100 mmHg ตตตตตตตตตตตตตตตตตตตตตตตตตตต
?
ตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต1T
P1
= 2T
2P
P1 = 380 mmHg
P2 = 380 - 100 = 280 mmHg
T1 = 273 + 40 = 313 K
T2 = ? K
ตตตตตตตตตตตตตตตตตตตต
313
380
= 2T
280
T2 = 230.6 K
ตตตตตตตตตตตตตตตตตต230.6 ตตตตตตตตตต-42.4 ตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตต7.ตตตตตตตตตตตตตตตตตตตตตตตตตต27 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต1.5 ตตตตตตตตตตตตตตตตต0.8 atm ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต2.5 ตตตตตตต0 0
C ตตตตตตตตตตตตตตตตตตตตตต?
ตตตตตตต
ตตตตตตตตตตตต1T
1V1P
= 2T
2V2P
P1 = 0.8 atm
P2 = ? atm
V1 = 1.5 dm3
V2 = 2.5 dm3
T1 = 273 + 27 = 300 K
T2 = 273 K
ตตตตตตตตตตตตตตตตตตตตต 273
2.5x2P
300
1.5x0.8 =
P2 = 0.427 atm
23
ตตตตตตตตตตต8 ตตตตตตตตตตNe 800 cm3
ตตตSTP
ต. ตตตตตตตตตตตตตตตตตตต30 0
C 152 mmHg
ต. ตตตตตตตตตตตตตตตตตตตตตตตตตตตตต500 cm3
ตตตตตตต2 atm ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตต ตตตSTP ตตต0 ตตตตตตตตตตตต1 atm
ตตตตตตตตตตตตตตต1T
1V1P
= 2T
2V2P
ต. P1 = 760 mmHg
P2 = 152 mmHg
V1 = 800 cm3
V2 = ? dm3
T1 = 273 K
T2 = 273 +30 = 303 K
ตตตตตตตตตตตตตตตตตตตตต 303
2x V152
273
0.8x760 =
V2 = 4.44 dm3
ตตตตตตตตตตตตตตตตตตตตตต4.44 ตตตตตตต30 0
C 152 mmHg
ต. P1 = 1 atm
P2 = 2 atm
V1 = 800 cm3
V2 = 500 cm3
T1 = 273 K
T2 = ? K
ตตตตตตตตตตตตตตตตตตตตต 2T
500x2
273
800x1 =
T2 = 341.3 K
ตตตตตตตตตตตตตตตตตตตตตตตตตต341.3 K
ตตตตตตตตตตต9 ตตตตCO2 ตตตตตตตตตตตตตต30 ตตตตตตตตตตตต0.5 atm ตตตตตตตตตตตตต10.0 ตตตต
ต. ตตตตCO2 ตตตตตตตตตตตตตตตตตตตต
ต. ตตตตCO2 ตตตตตตตตตตตตตตตตตตตตต
24
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตPV = nRT
ต. ตตต PV = nRT = M
W
RT
P = 0.5 atm
w = ? g
R = 0.082 dm3
atm K-1
mol-1
V = 10.0 dm3
M = ตตตตตตตตตต= 44
T = 273 +30 303 K
ตตตตตตตตตตตตตตตตตต0.5 x 10.0 = 44
W
x 0.082 x 303
w = 8.85 g
ตตตตตตตตตตตตตตตตตตตCO2 8.85 ตตตต
ต. ตตต PV = 2310x6.02
NRT
N = ตตตตตตตตตตตตต
0.5x 10.0 = 2310x6.02
303x0.082xN
N = 1.21 x 1023
ตตตตตตต
ตตตตตตตตตตตตตตตตตตตCO2 1.21 x 1023
ตตตตตตต
2 ตตตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตต2 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ก. กกกกกกก(diffusion) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ก. กกกกกกกกกกก(effusion) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต(ideal flow) ตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตeffusionmeter
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตต(Graham ,
s law of diffusion)
25
ตตตตตตตตตตตตตตตตตตตตตตตตตต(Graham ,
s law of effusion) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต(Thomas
Graham) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
“ ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต”
ตตตตตตV = ตตตตตตตตตตตตตตตตตตต
M = ตตตตตตตตตตตตตตตตต
d = ตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
M
1V α ตตต d
1V α
ตตตต M
kV = ตตต d
kV
/
=
ตตตตตk , k/
ตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต(absolute) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต2 ตตตต
ตตต M
kV =
ตตตตต, ตตตตตตตตตตต1 1M
k
1V =
ตตตตตตตตตตต2 2M
k
2V =
ตตตตตตต 1M
2M
2V
1V
=
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
1d
2d
2V
1V
=
ตตตตตตตตตตตตตตตตตตตตต
1M
2M
2V
1V
=
1d
2d
=
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต dM α (ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต)
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
26
(t)ตตตต
(s)ตตตตตตตV = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
1M
2M
2s
2t
.
1t
1s
2V
1V
==
1d
2d
=
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต( s1 = s2 ) ตตตตต
1M
2M
1t
2t
2V
1V
==
1d
2d
=
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต( s1 = s2 ) ตตตตต
1M
2M
2s
1s
2V
1V
==
1d
2d
=
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตCH4 ตตตCO2 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตCH4 ตตตตตตตตตตตตตตตตตตตตCO2 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตCH4
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตต1 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
Ne, N2 , NO , O2 , Ar
ตตตตตตต
ตตตตตตตตตตตตตตตตตตตตต“ ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตตตตตตตตNe = 20 , N2 = 28 , NO = 30, O2 = 32 ,
Ar = 39
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต Ne < N2 < NO < O2 < Ar
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต Ne > N2 > NO > O2 > Ar
กกกกกกกกกกก2 ตตตตตตตX ตตตตตตตตตตตตตตตตตตต81 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต30 ตตตตตตตตตตตตตตต2 ตตตตตตตตตตY ตตตตตตตตตตตตตตตตตตต25 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต4 ตตตตตต
ตตตตตตต
ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต
27
1M
2M
2s
2t
.
1t
1s
2V
1V
==
s1 = ตตตตตตตตตตX ตตตตตตตตตต30 cm s2 = ตตตตตตตตตตY ตตตตตตตตตต? cm
t1 = ตตตตตตตX ตตตตตตตตตต2 ตตตตตต t2 = ตตตตตตตY ตตตตตตตตตต4 ตตตตตต
M1 = ตตตตตตตตตตตตตX = 81 M2 = ตตตตตตตตตตตตตY = 25
ตตตตตตตตตตตตตตตต 81
25
2s
4x2
30 =
s2 = 108 cm
ตตตตตตตตตตตตตตตY ตตตตตตตตตตตตต108 ตตตตตตตตต
ตตตตตตตตตตต3 ตตต25 ตตตตตตตตตตตต1 atm ตตตตA ตตตตตตตตตตตตตตตตต3 ตตตตตตตตตตตB ตตตตตตตA ตตตตตตต50 cm ตตตตตต20 ตตตตตต
ต. ตตตตB ตตตตตตตตตตตตตตตตcm/ตตตตตต
ต. ตตตตตตตตตตตตตตตตตB ตตตตตตตตตตต80 cm ตตตตตตตตตตตตตตตตตตตตตต
ตตตตตตต
ต. ตตต Ad
Bd
BV
AV
=
ตตตตตต20
cm50
At
AS
AV == = 2.5 cm/ตตตตตต
1
3
Ad
Bd
ตตตต3
1
Bd
Ad
==
ตตตตตตตตตตตตตตตตตตตตตตตตตตตต
3
1
BV
2.5 =
VB = 4.33 cm/ตตตตตต
ต. ตตต 1d
2d
Bs
Bt
.
At
As
BV
AV
==
SA = 50 cm S B = 80
cm
tA = 20 ตตตตตต tB = ?
ตตตตตตตตตตตตตตตตตตตตตตตตตตตต
3
1
80
Bt
x20
50 =
28
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid
gas liquid-solid

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Good Stuff Happens in 1:1 Meetings: Why you need them and how to do them well
 
Introduction to C Programming Language
Introduction to C Programming LanguageIntroduction to C Programming Language
Introduction to C Programming Language
 

gas liquid-solid

  • 1. กกกกกกกกกกกกกกกกกก สสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห สสสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห กกกกกกกกกกก หหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหหหหหหหหหหหหหหหหหหหหหห สสสสสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห สสสสสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห สสสสสสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหห) หหหหหหห(หหหห) หหหหหหห(หหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหห หหหหหหห หหหหหหห หหหห หหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหห
  • 2. หหหหหหห หหหหหหหหหหห (หหห 250 C) หหหหหหหหหหห ( 0 C ) หหหหหหหห ( 0 C ) หหหหหหห หหหหหหหห หหหห หหหหหห หหหหหหห หหหหหหหห หหหหหหห หหหหหหห หหหหหหห หหหหหหห หหหห หหหห 97.8 838 -38.4 -7.2 -269.7 -210 892 1440 357 58 -268.9 -195.8 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห97.8 0 C หหหหหหหหหห892 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหห97.8 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห97.8 - 892 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 892 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหห25 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห2 หหหหหหหหหหหหหหหหหหหห25 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห25 0 C หหหหหหหหหหหหหหหหหหหห250 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห25 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(CH3COOH) หหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหห117.9 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห16.6 - 117.9 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห16.6 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห10 mmHg หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห50 0 C หหหหหหห กกกกกกกกกกกกก กกกกกกกกกกกกกกกกกกกกกกกกกกกก 1.กกกกกกกกกกกกกกกกกกกกกกกกกกกกกกกกหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห10 หหหหหหหหหหหหหหหหหหหหหหหหห10 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 2.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Random Motion) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 3.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 4.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 5.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหF2 (หหหหหหหหหหหห) , Cl2 (หหหหหหหหหหหหหห) , Br2 (หหหหห) , I2 (หหหหหหหหห) , NO2 (หหหหหหหหหหหห) , SO2 (หหหหหหหหหหหหหหหหห) หหหH2S (หหหหหหหหหหหหหหหหหห) หหหหหหห 2
  • 3. 6.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 หหหหหหหหห22.4 หหหหหหห0 0 C , 1 atm หหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหT (หหหหหห) หหหt (หหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห100 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหห สสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสส 1.หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(0 C) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห100 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 0 C 2.หหหหหหหหหหหหหหหห(0 F) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห180 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 0 F 3.หหหหหหหหหหห(K) หหหหหหหหหหหหหหหหหหหหหหหหห(Absolute Temperature) หหหหหหหหหSI หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห100 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 K หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 หหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหห= 0 0 C = 273.15K = 32 0 F หหหหหหหหหหหหหหห= 100 0 C= 373.15 K = 212 0 F 375.15 273.15 0 (K) 100 0 -273.15 212 -32 -459.7 (0C) (0F) หหหหหห หหหหหหหห หหหหหหหหหหห หหหหหห4.2 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหห3 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห T = 273.15 + t T = 273.15 + 9 5 ( F - 32 ) t = 9 5 ( F - 32 ) 3
  • 4. หหหหหT = หหหหหหหหหหหหหห t = หหหหหหหหหหหหหหหห F = หหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห T = 273.15 + t T = 273.15 + 9 5 ( F - 32 ) t = 9 5 ( F - 32 ) หหหหหหหหหหหหหหหหหหหหหหหP หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Barometer) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 cm2 หหหหหหหหห100 cm หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 cm3 หหหหหหหหหหหหหหหหหหหหหหหหห76 cm หหหห760 mm หหหหหหหหหหหห1 หหหหหหหห(atm) หหหหหห4.3 หหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Nanometer)หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหห) 4
  • 5. หหหหหหหหหหหหหหหหหหห(หหหห. ) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(h) (หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหห2 หหหห(หหหห. ) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห2 หหหห(h) หหหหหหหหหหหหหหหหหหหหหหหห กกกกกกกกกกกกกกกกกกกกกกกกกกกกกก หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหห) หหหห1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหh หหหหหหหหห(หหหหห4.3 หหหหหห) หหห หหห(F) = หหหหหหห(m) x หหหหหหหหหหหหหหห(g) หหหหหหหหหห= หหหหหหหหหหห(V) x หหหหหหหหหหหหหหห(d) หหหหหหหหหหห F = mg = Vdg = (Ah)dg หหหหหA = หหหหหหหหหหหหหหหหหหหหห หหหหหหหหห หหหหหหห(P) = (A)หหหหหหห (F)หหห หหหหหหหหหหห P = dgA Ah = hdg หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห25 0 C หหหหหหหหหหหห76.1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห P = hdg = (76.1 cm) x (13.596 g/cm3 ) x (980.7 cm/s2 ) = 1.015 x 106 g/cm.s2 = 1.015 x 106 dyne/cm2 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห76 หหหหหหหหหหหห0 0 C หหหหหหหหหหหหห1 หหหหหหหห( 1 atm) หหหหหหหหหหหหหห( 1 atm) หหหหหหหหหdyne/cm2 หหหหหหหหหหหห P (1 atm) = hdg = (76.0 cm) x (13.596 g/cm3 ) x (980.7 cm/s2 ) = 1.013 x 106 dyne cm-2 5
  • 6. หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหatm หหหหdyne cm-2 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห( N/cm2 ) , หหหหหหหหหหหหหหหหหห(N/m2 ) หหหหหหหหหหหหหหหหหหหหหหห S.I. ( 1 Pa = 1 kg/m. s2 ), หหหหหหหหหหหหหหหหห(pound per square inches) หหหหp.s.i ) , mm Hg หหหหtorr หหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหatm หหหmm Hg หหหPa หหหหหหหหหหหหหหหหหหหหหหหหหหห 1 atm = 760 mm Hg = 76 cm Hg = 760 torr = 17.7 p.s.i = 1.013 x 105 Pa = 1.013 x 105 N/m2 = 1.013 x 106 dyne cm-2 กกกกกกกกกกกกกกกกกกกกกกกกก หหหหหหหหหหหหหหหหSTP หหหหหหหหหหหหStandard Temperature and Pressure หหหห NTP หหหหหหหหหหหหNormal Temperature and Pressure หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหห00 C หหหห273.15 K (273 K หหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหห1 atm หหหห760 mm Hg กกกกกกกกกกกกกก หหหหหหหหหหหหหหหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(V) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห( หหห) หหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหdm3 หหหcm3 หหหหหหหหหหหหหS.I หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 1 หหหห = 1000.027 cm3 = 1 dm3 (หหหหหหหหห) 1 หหหหหหหหห= 1.000027 cm3 = 1 cm3 (หหหหหหหหห) หหหหหหหหหหห1 dm3 = 103 cm3 = 1 หหหห= 103 หหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห กกกกกกกกกกกกก 6
  • 7. หหหหหหหหหหหหหหหหหหหหหหหหหหหหห2 หหหหหหหหหหหห ส. สสสสสสสสสสส( ideal gas) หหหหหหหหหหหหหหห(perfect gas) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห ส. สสสสสสสส(real gas) สสสสสสสหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 , O2 CO2 , หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 1 กกกกกกกกกกกกกก หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห ก. กกกกกกกกกก(Boyle , s Law) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห.ห. 1662 (ห.ห. 2205) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Robert Boyle) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห “ หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห” หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห V α P 1 หหหหหหหหหหหหหหหหหหหหหหหห หหห V = P k หหหหPV = k หหหหหV = หหหหหหหหหหหหหห P = หหหหหหหหหหหหหห k = หหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหห P1V1 = P2V2 = P3V3 = …….. หหหk หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหk หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหk หหหหหหหหหหหหหหหหหหหหหk หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP , V หหหหหหหหห หหหหหหหหPV = k หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห“ หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห” หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหห 7
  • 8. หหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหห หหหหหห1 หหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Hyperbolar) หหห V = P k หหหหหP = 0 หหห V = ∞ V = 0 หหห P = ∞ หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหหหหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Isotherm) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Isothermal Process) หหหหหห4.6 หหหหหหหหหหหหหหหหหหหP หหหV หหหหหT หหหn หหหหห หหหหหห2 หหหหหหหหหหหหหหหหหหหหหP หหหV 1 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(Origin) หหหหหหหหหหหหหหหหห V = P k = k P 1 + 0 หหหหP = k V 1 + 0 8
  • 9. หหหหหหหหหหหหหหหหหหหหหหหหหหหy = ax + b หหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV 1 หหหหV หหหP 1 หหหหหหหหหหหหหหหหหหหหหหหหหหหห(Slope = k หหหหหหหหหหห (Intercept) = 0 หหหหหหหหหหหหหหหหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(หหหหหหหหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหห4.7 หหหหหหหหหหหหหหหหหหหP หหหV 1 (หหหหV หหหP 1 ) หหหหหห3 หหหหหหหหหหหหหหหหหหหหหPV หหหP หหหหPV หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหP (หหหหV หหหหหหหหห) หหหหหหหหหหหหหหหหหหหหหหหห= 0 หหหหหหหหหหหหหหหหหหหหหหหหหหห PV = k หหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหPV หหหP (หหหหPV หหหV) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห3 หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห(P1V1 ≠ P2V2 ) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 , He , N2 , CH4 หหหCO2 หหห40 0 C หหหหหหหหหหหหหหหหหหหหห0 - 800 atm หหหหหหหหหหหหหหPV หหหP หหหหหหหหหหห 9
  • 10. หหหหหหหหหหหหหหหหหหหหหหPV หหหP หหหหหหหหหหห หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหP หหหV หหหหหหห1 หหหหหหหหหหหหหหหหหหหหหห หหหหHe P (atm ) V (dm3 ) PV (dm3 atm) -100 0 C 0 0 C 100 0 C -100 0 C 0 0 C 100 0 C 5 25 50 75 100 2.85 1 0.57 9 0.29 6 0.20 1 0.15 4 4.48 9 0.90 7 0.45 9 0.31 0 0.23 6 6.12 4 1.23 4 0.62 3 0.41 9 0.31 7 14.2 35 14.4 93 14.7 97 15.1 06 15.4 20 22.4 47 22.6 84 22.9 80 23.2 76 23.5 73 30.6 21 30.8 48 31.1 33 31.4 17 31.7 02 10
  • 11. หหหหH2 5 25 50 75 100 2.84 8 0.57 7 0.29 4 0.19 9 0.15 3 4.49 1 0.91 0 0.46 2 0.31 3 0.23 8 6.13 2 1.23 9 0.62 7 0.42 3 0.32 1 14.2 40 14.4 34 14.7 01 14.9 92 15.3 09 22.4 57 22.7 39 23.0 97 23.4 61 23.8 30 30.6 62 30.9 73 31.3 63 31.7 52 32.1 41 ก. กกกกกกกกกกกก(Charles , law) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหห.ห. 1787 (ห.ห. 2330) หหหหหหหหหหหห(Jacques Charles) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหH2 , หหหหห, O2 , หหหCO2 หหหหหหหหหหหหหห0 - 80 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห หหหหหหหหหหหหหหห(Joseph Gay - Lussac) หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห1 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห273.15 1 หหหหหหหหหหหหหหหหห0 0 C หหหหหหV0 = หหหหหหหหหห0 0 C V = หหหหหหหหหหt 0 C หหหหหหหหหหหหหหหหหหหหหหt 0 C หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห V = V0 + 273.15 1 V0T = V0( 1 + 273.15 t ) = V0 273.15 t)(273.15+ หหหหหห T = 273.15 + t T0 = 273.15 หหหหห V = V0( 0T T ) หหหห T V = 0 0 T V หหหหหหหหหหหหหหหหหหหหหหหหหห0 0 T V หหหหหหหหหหหหT V หหหหหหหหหหหหหหหหห T V = k หหหหหหหV หหหหหหหหหหหT หหหหหหหหT หหหหหหหหหV หหหหหหหหหหหT หหV หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห “ สสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสสส” หหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหหห 11
  • 12. V α T (เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ) เเเเเเเเเเเ V = kT เเเเ T V = k เเเเ 1 1 T V = 2 2 T V = n n T V = ……. เเเเเ k เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเT T เเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ2 เเเเเเเเเ เเเเเเ1 เเเเเเเเเเเเเเV เเเT เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV = kT เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ= k เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ“ เเเเเเเเเเเเเเเเ(Isobar)” เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เ. เเเเเเเเเเเเเเเเ( P เเเเเเเเเเ) เ. เเเเเเเเเเเเเเเ(P เเเเเเเ) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเ2 เเเเเเเเเเเเเเเเเเเเเV เเเt (0 C) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ 12
  • 13. เ. เเเเเเเเเเเเเเเเ( P เเเเเเเเเเ) เ. เเเเเเเเเเเเเเเ(P เเเเเเเ) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ2 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ-273.15 0 C เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ-273.15 0 C เเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเ= 273.15 + เเเเเเเเเเเเเเเเ T = 273.15 + t เเเเ T = 273 + t เเเเเเเเT = 273 + t เเเเเเเเเเเเเเเเV = kT เเเเเ V = kT = k(273 + t ) เเเเเเเเเเเ V = kt + 273k เเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(y = ax + b) เเเเเเเเเเเเเเเเเเเเเV เเเt เเเเเเเเเเเเ= 273k เเเเเเเเเเ= k เเเเเเเเเเเเ) เเเเเเเเเเเเเเเเเเเV เเเT เเเV เเเt เเเเเเเเเเเเเเเเเเเเเเเเ 13
  • 14. เเเเเเ4.2 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเ0 เเเเเเเเเเ-273.15 0 C เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ0 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเ ค.คคคคคคคคคคคคคคค(Gay - Lussac , s Law) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(Amanton s law) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(P) เเเเเเเเเเเ(T) เเเเเเเเเเเเเเ “ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ” เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ P α T เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเ P = kT เเเเT P = k เเเ 1T P1 = 2T 2P เเเเ 2P 1P = 2T 1T เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP เเเT เเเเเเเเเเเเHe 1 เเเเเเเเเเเเเ22.4 เเเเ P (atm) 0.5 0.6 0.8 1.0 1.2 1.5 14
  • 15. T(K) 136.5 163.8 218.4 173.0 327.6 409.5 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP เเเT เเเP เเเt เเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเP เเเT เเเP เเเt ค. คคคคคคคคคคคคคค(Avogadro , s law) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ “ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(เเเเเเเเเ) เเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ V α n เเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเV = kn เเเเ n V = k เเเ 1n 1V = 2n 2V เเเเ 2V 1V = 2n 1n เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเn เเเN2 เเเ1 atm 273 K n (เเเ) 0.1 0.2 0.5 0.8 1.0 2.0 V (dm3 ) 2.24 4.48 11.2 17.92 22.4 44.8 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเV เเเn เเเเเเเเเเเ 15
  • 16. เเเเเเเเเเเเเเเเเเเเเเV เเเn ค. คคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคค (Combined gas law : equation state of ideal gas) คคคคคคคคคเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V เเเT เเเเเเเเเเเเเ เเเเเเเเเเเเเ V α P 1 เเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเเ V α T เเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเ V α P T เเเเเเเเเเเเเ เเเเเเเเเเเ V = k P T เเเเ T PV = k เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ 1T 1V1P = 2T 2V2P = …… เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , T เเเV เเเเเเเเเเเเเเเเเเเเเเเเเเเP , V เเเเT เเเเเเเเเเเเเเเเเเเเเเเเ(n) เเเเเเเเเเเเ คคคคคคคคคคคคคคคคคคคคคคค เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ1T 1V1P = 2T 2V2P เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ 16
  • 17. เเเเเเเเเเเเเเเเเเเเเเเV α P T เเเเเเเเเเเเเเเเเ V α n เเเเเเเเเเเเเเเเ V α P nT เเเเ V = P RnT เเเเ PV = nRT เเเเเเเเเเPV = nRT เเเเเเ“ เเเเเเเเเเเเเเเเเเเเเเเ” เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ R เเเเเเเเเเเเเเเเเเเเเเเเเเเ(Universal constant) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ R เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเR เเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเR เเเเเเเเเเเเ เเเเR = 0.082 atm . l . K-1 . Mol-1 เเเเเเเเเเเเเเเเเเเเเเเเเเO2 , H2 , CO2 , เเเเเเเเเเเเเเ V เเเเl (เเเเ) , P เเเเatm , T เเเเK , เเเn เเเเmol เเเเเเเเเเเR = 0.082 เเเเเเเ คคคคคคคคR เเเR เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ R = nT PV เเเเเเเเเเเเเเเเเ1 เเเเเเเเเเเเเเเเ22.414 เเเเเเเSTP ( 00 C , 1 atm) เเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเR เเเเเเ R = nT PV = K)(273.15)mol.1( l.)22.414()atm1( = 0.08205 atm . l . K-1 . Mol-1 (เเเเR = 0.082 atm . l . K-1 . Mol-1 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ) เเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเR เเเเเเเเเเเเเเเ R = nT PV = K)(273.15)mol.1( .)cm22414()atm1( 3 = 82.05 atm . cm3 . K-1 . Mol-1 เเเR เเเเเเเเเเเเเเเเเเเเเเเเP , V , T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเ4.6 เเเเเเเเเเเเเเเเเเเเเเเเเเเ( T เเเเเเเเเเ, n เเเเเเเ) 17
  • 18. P V R atm atm mm.Hg l cm3 cm3 0.082 l. atm . K-1 . Mol-1 82.05 cm3 atm . K-1 . Mol- 1 62360 cm3 mm.Hg. K-1 . Mol-1 R เเเเเเเergs = 8.314 x 107 ergs K- 1 mol-1 R เเเเเเเJoule = 8.314 JK-1 mol-1 R เเเเเเเcalory = 1.987 cal K-1 mol-1 เเเเเเเเ1 J = 107 ergs 1 cal = 4.184 J. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเR = 0.082 l. atm . K-1 . Mol-1 คคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคค เเเเเเเเเเเเเเเเเเเเเเเเ n = M W = 2310x6.02 N เเเเเN = เเเเเเเเเเเเเ M = เเเเเเเเเเ W = เเเ n = เเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเPV = nRT เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(d) เเเ PV = nRT = M W RT เเเเเเเเเเเ M = P RT V W. = P RTd เเเเ d = RT PM เเเเเ d = V W = เเเเเเเเเเเเเเเเเเ(เเเเเเเเเg/dm3 ) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเP , V, T เเเn เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเเเเเเเเเเเเP , V, T เเเw (เเเเd) เเเเM เเเเเเเเเเเเเเเเเเเเเเเเเM เเเเเเเเd เเเเเเเเเเเเเเเ 18
  • 19. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เเเ d = RT PM เเเเเเเเเเเเเเเเเเเเเเเM เเเเเเเเเ เเเT เเเP เเเเเเเ เเเเเd1 = 1RT 1P M เเเ d2 = 2RT 2P M 1T2P 2T1P 2d 1d = เเเเ 2P 2T2d 1P 1T1d = เเเเเเเเเเเเเเเเเเเเเเเเเเเT เเเP เเเเเเเเเเเเ P RT 1d1M = เเเ P RT 2d2M = เเเเเ 2d 1d 1M 1M = เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ(N) เเเเเเเเเเเเเเเเP , V , เเเT เเเเเเเเเเเเเเ PV = nRT = 2310x6.02 NRT เเเเ N = 23 10x6.02RT PV คคคคคคคคคคคคคคคคคคคคคคคคคคค คคคคคคคคคคค1 เเเเN2 เเเเเเ10.0 dm3 เเเ25 0 C เเเเเเเเเเเเเเเเเ0.40 atm เ. เเเเเเเเเเเเเเเเเเเ2.0 atm เเเเเเเเเเเเเเเเเเเเเ? (เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ) เ. เเเเเเเเเเเเเเเเเเเเเเเเเเเเ5.0 dm3 เเเเเเเเเเเ25 0 C เเเเเเเเเเเเเเเเเเเเเเเเเเเเเ? เเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เ. เเเP1V1 = P2V2 P1 = 0.40 atm P2 = 2.0 atm V1 = 10.0 dm3 19
  • 20. V2 = ? เเเเเเเเเเเเเเเเเ 0.40 x 10.0 = 2.0 x V2 V2 = 2.0 dm3 เ. เเเเเเเเเเเเเเเเเเเเเเเ. P1 = 0.40 atm P2 = ? atm V1 = 10.0 dm3 V2 = 5.0 dm3 เเเเเเเเเเเเเเเเเ 0.40 x 10.0 = 5.0 x P2 P2 = 0.8 atm คคคคคคคคคคค2 เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ30 0 C เเเเเเเเเเเเเ380 mm.Hg เเเเเเเเเ500 cm3 เ. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเcm3 เ. เเเเเเเเเเเเเเเเเเเเเเเเเเ100 cm3 เเเเเเเเเเเเเเเเmm.Hg เเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ เ. เเเP1V1 = P2V2 P1 = 380 mm.Hg P2 = 380 + 380 = 760 mm.Hg V1 = 500 cm3 V2 = ? cm3 เเเเเเเเเเเเเเเเเ 380 x 500 = 760 x V2 V2 = 250 cm3 เเเเเเเเเเเเเ= 500 - 250 = 250 cm3 เ. เเเเเเเเเเเเ100 cm3 P1 = 380 mm.Hg P2 = ? mm.Hg V1 = 500 cm3 V2 = 500 + 100 cm3 เเเเเเเเเเเเเเเเเ 380 x 500 = P2 x 600 20
  • 21. P2 = 316.7 mm.Hg เเเเเเเเเเเเเ= 380 - 316.7 = 63.3 mm.Hg คคคคคคคคคคค3 เเเเHe เเเเเเเเเเเเเเเเเเเเเเเเเเ20 0 C เเเเเเเเเเเเเ400 mmHg. เเเเเเเเเเHe เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ20 dm3 เเเเเเเเเเเเเ150 mmHg. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ? เเเเเเเ เเเเเเเเเเเเเP1V1 = P2V2 P1 = 400 mm.Hg P2 = 150 mm.Hg V1 = ? dm3 V2 = 20 dm3 เเเเเเเเเเเเเเเเเ 400 x V1 = 150 x 20 V1 = 7.5 dm3 เเเเเเเเเเเเเเเเเเเเเเ7.5 เเเเ คคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคคค คคคคคคคคคคค4. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ200 cm3 เเเ27 0 C เเเเเเเ700 mmHg เ. เเเเเเเเเเเเเเเเเเเเเ40 0 C เเเเเเเเเเเเเเเเเ(เเเเเเเเเเเเ) เ. เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ120 cm3 เเเ700 mmHg เเเเเเเเเเเเเเเเเเเเเเเเเเ? เเเเเเเ เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ1 1 T V = 2 2 T V เ. V1 = 200 cm3 T1 = 273 + 27 = 300 K V2 = ? cm3 T2 = 273 + 40 = 313 K เเเเเเเเเเเเเเเเเ 300 200 = 313 V2 V2 = 208.7 cm3 เ. V1 = 200 cm3 21
  • 22. T1 = 273 + 27 = 300 K V2 = 120 cm3 T2 = ? K เเเเเเเเเเเเเเเเเ 300 200 = 2T 120 T2 = 180 K เเเเเเเเเเเเเเเเเเ180 K เเเเ-93 0 C คคคคคคคคคคค5 เเเเเเเเเเเเ2.5 เเเเเเเ1 atm 30 0 C เ. เเเเเเเเเเเเเเเเ10 0 C เเเเเเเเเเเเเเเเเเเเเ เ. เเเเเเเเเเเเเเเเเเเเเเเเ300 cm3 เเเเเเเเเเเเเเเเเเเ0 C (เเเเเเเเเเเเเเเเเเเเเ2 เเเเเเเเเเเเเเเเเเเเเเ) เเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเเ1 1 T V = 2 2 T V เ. เเเเเเเเเเเเเ10 0 C V1 = 2.5 dm3 T1 = 273 + 30 = 303 K V2 = ? dm3 T2 = 273 + (30 + 10 ) = 313 K เเเเเเเเเเเเเเเเเ 303 2.5 = 313 2V V2 = 2.583 dm3 เ. เเเเเเเเเเเ300 cm3 = 0.300 dm3 V1 = 2.5 dm3 T1 = 273 + 30 = 303 K V2 = 2.5 - 0.300 dm3 T2 = ? K เเเเเเเเเเเเเเเเเ 303 2.5 = 2T 2.200 22
  • 23. T2 = 266.6 K ตตตตตตตตตตตตตตตตตต266.6 K ตตตตตตตตตตต266.6 - 273 = -6.4 0 C ตตตตตตตตตตตตตตตตตตตตตตตตตตต30 - (-6.4) = 36.4 0 C ตตตตตตตตตตต6 ตตตตตตตตตตตตตตตA 5 ตตตตตตตตตตตตตตตตตตตตตตตตตตตต40 0 C ตตตตตตต380 mmHg ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต10 dm3 ตตตตตตตตตตตตตตตตตตตตตตตต100 mmHg ตตตตตตตตตตตตตตตตตตตตตตตตตตต ? ตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต1T P1 = 2T 2P P1 = 380 mmHg P2 = 380 - 100 = 280 mmHg T1 = 273 + 40 = 313 K T2 = ? K ตตตตตตตตตตตตตตตตตตตต 313 380 = 2T 280 T2 = 230.6 K ตตตตตตตตตตตตตตตตตต230.6 ตตตตตตตตตต-42.4 ตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตต7.ตตตตตตตตตตตตตตตตตตตตตตตตตต27 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต1.5 ตตตตตตตตตตตตตตตตต0.8 atm ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต2.5 ตตตตตตต0 0 C ตตตตตตตตตตตตตตตตตตตตตต? ตตตตตตต ตตตตตตตตตตตต1T 1V1P = 2T 2V2P P1 = 0.8 atm P2 = ? atm V1 = 1.5 dm3 V2 = 2.5 dm3 T1 = 273 + 27 = 300 K T2 = 273 K ตตตตตตตตตตตตตตตตตตตตต 273 2.5x2P 300 1.5x0.8 = P2 = 0.427 atm 23
  • 24. ตตตตตตตตตตต8 ตตตตตตตตตตNe 800 cm3 ตตตSTP ต. ตตตตตตตตตตตตตตตตตตต30 0 C 152 mmHg ต. ตตตตตตตตตตตตตตตตตตตตตตตตตตตตต500 cm3 ตตตตตตต2 atm ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตต ตตตSTP ตตต0 ตตตตตตตตตตตต1 atm ตตตตตตตตตตตตตตต1T 1V1P = 2T 2V2P ต. P1 = 760 mmHg P2 = 152 mmHg V1 = 800 cm3 V2 = ? dm3 T1 = 273 K T2 = 273 +30 = 303 K ตตตตตตตตตตตตตตตตตตตตต 303 2x V152 273 0.8x760 = V2 = 4.44 dm3 ตตตตตตตตตตตตตตตตตตตตตต4.44 ตตตตตตต30 0 C 152 mmHg ต. P1 = 1 atm P2 = 2 atm V1 = 800 cm3 V2 = 500 cm3 T1 = 273 K T2 = ? K ตตตตตตตตตตตตตตตตตตตตต 2T 500x2 273 800x1 = T2 = 341.3 K ตตตตตตตตตตตตตตตตตตตตตตตตตต341.3 K ตตตตตตตตตตต9 ตตตตCO2 ตตตตตตตตตตตตตต30 ตตตตตตตตตตตต0.5 atm ตตตตตตตตตตตตต10.0 ตตตต ต. ตตตตCO2 ตตตตตตตตตตตตตตตตตตตต ต. ตตตตCO2 ตตตตตตตตตตตตตตตตตตตตต 24
  • 25. ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตPV = nRT ต. ตตต PV = nRT = M W RT P = 0.5 atm w = ? g R = 0.082 dm3 atm K-1 mol-1 V = 10.0 dm3 M = ตตตตตตตตตต= 44 T = 273 +30 303 K ตตตตตตตตตตตตตตตตตต0.5 x 10.0 = 44 W x 0.082 x 303 w = 8.85 g ตตตตตตตตตตตตตตตตตตตCO2 8.85 ตตตต ต. ตตต PV = 2310x6.02 NRT N = ตตตตตตตตตตตตต 0.5x 10.0 = 2310x6.02 303x0.082xN N = 1.21 x 1023 ตตตตตตต ตตตตตตตตตตตตตตตตตตตCO2 1.21 x 1023 ตตตตตตต 2 ตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตต2 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ก. กกกกกกก(diffusion) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ก. กกกกกกกกกกก(effusion) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต(ideal flow) ตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตeffusionmeter ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตต(Graham , s law of diffusion) 25
  • 26. ตตตตตตตตตตตตตตตตตตตตตตตตตต(Graham , s law of effusion) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต(Thomas Graham) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต “ ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต” ตตตตตตV = ตตตตตตตตตตตตตตตตตตต M = ตตตตตตตตตตตตตตตตต d = ตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต M 1V α ตตต d 1V α ตตตต M kV = ตตต d kV / = ตตตตตk , k/ ตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต(absolute) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต2 ตตตต ตตต M kV = ตตตตต, ตตตตตตตตตตต1 1M k 1V = ตตตตตตตตตตต2 2M k 2V = ตตตตตตต 1M 2M 2V 1V = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต 1d 2d 2V 1V = ตตตตตตตตตตตตตตตตตตตตต 1M 2M 2V 1V = 1d 2d = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต dM α (ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต) ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต 26
  • 27. (t)ตตตต (s)ตตตตตตตV = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต 1M 2M 2s 2t . 1t 1s 2V 1V == 1d 2d = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต( s1 = s2 ) ตตตตต 1M 2M 1t 2t 2V 1V == 1d 2d = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต( s1 = s2 ) ตตตตต 1M 2M 2s 1s 2V 1V == 1d 2d = ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตCH4 ตตตCO2 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตCH4 ตตตตตตตตตตตตตตตตตตตตCO2 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตCH4 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตต1 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต Ne, N2 , NO , O2 , Ar ตตตตตตต ตตตตตตตตตตตตตตตตตตตตต“ ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต ตตตตตตตตตตตตตNe = 20 , N2 = 28 , NO = 30, O2 = 32 , Ar = 39 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต Ne < N2 < NO < O2 < Ar ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต Ne > N2 > NO > O2 > Ar กกกกกกกกกกก2 ตตตตตตตX ตตตตตตตตตตตตตตตตตตต81 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต30 ตตตตตตตตตตตตตตต2 ตตตตตตตตตตY ตตตตตตตตตตตตตตตตตตต25 ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต4 ตตตตตต ตตตตตตต ตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตตต 27
  • 28. 1M 2M 2s 2t . 1t 1s 2V 1V == s1 = ตตตตตตตตตตX ตตตตตตตตตต30 cm s2 = ตตตตตตตตตตY ตตตตตตตตตต? cm t1 = ตตตตตตตX ตตตตตตตตตต2 ตตตตตต t2 = ตตตตตตตY ตตตตตตตตตต4 ตตตตตต M1 = ตตตตตตตตตตตตตX = 81 M2 = ตตตตตตตตตตตตตY = 25 ตตตตตตตตตตตตตตตต 81 25 2s 4x2 30 = s2 = 108 cm ตตตตตตตตตตตตตตตY ตตตตตตตตตตตตต108 ตตตตตตตตต ตตตตตตตตตตต3 ตตต25 ตตตตตตตตตตตต1 atm ตตตตA ตตตตตตตตตตตตตตตตต3 ตตตตตตตตตตตB ตตตตตตตA ตตตตตตต50 cm ตตตตตต20 ตตตตตต ต. ตตตตB ตตตตตตตตตตตตตตตตcm/ตตตตตต ต. ตตตตตตตตตตตตตตตตตB ตตตตตตตตตตต80 cm ตตตตตตตตตตตตตตตตตตตตตต ตตตตตตต ต. ตตต Ad Bd BV AV = ตตตตตต20 cm50 At AS AV == = 2.5 cm/ตตตตตต 1 3 Ad Bd ตตตต3 1 Bd Ad == ตตตตตตตตตตตตตตตตตตตตตตตตตตตต 3 1 BV 2.5 = VB = 4.33 cm/ตตตตตต ต. ตตต 1d 2d Bs Bt . At As BV AV == SA = 50 cm S B = 80 cm tA = 20 ตตตตตต tB = ? ตตตตตตตตตตตตตตตตตตตตตตตตตตตต 3 1 80 Bt x20 50 = 28