2. 10
10.1 F
F ˈ ˂
F ˈ F F (Q) F ˈ (J)
- F 1 (= 4.186 J ) F F 1
1° C
10.1.1
ˈ F F
F F F F F
F F F
10.2.1 F F
F F ˈ F F F F F
F F F F F
F F F
1. (° C)
2. (K) ˈ F F FF F F F ( ˈ F
SI)
K °C
373.16 100
F F K = C + 273
273.16 0
F
C=
۱ ܀ ۴ି R= F
= =
ૢ F= F
K=
– F ˆ F www.schoolDD.com 1
3. 10.1.2 F
1. F (C) F F
ˈ F F ˈ F (J/K)
m
〉 ∆T ઢۿ
C=
∆Q ઢ܂
2. F (c ) F F 1 F
ˈ F F ˈ F (J/kg K)
ઢۿ
〉 ∆T
m
c=
∆Q
ܕઢ܂
F FF F F m ΔT F F
Q= F (J)
m= (kg)
Q = mc∆T
c= F (J/kg K)
ΔT = (K ˚C)
- F (C) F F F C F C F
- F (c) F F ˈ
F c (J/kg K)
4186
(-10˚C 0˚C) 2100
900
450
390
140
130
– F ˆ F www.schoolDD.com 2
4. F 1 F F 100 25˚C ( c = 390
J/kg K)
. ˈ 45 ˚C
. ˈ 15 ˚C
. F F F F F
Q = mc∆T
= 0.10x390x(45-25)
Q = 780 J Ans
. F F F
Q = mc∆T
= 0.10x390x(25-15)
Q = 390 J Ans
10.1.4 F
F F F F
F F F
F
s
- ˈ F
F F F F F F F
10.1.5 F
3
F F F F F
F F
F F F F F
F F F F F
F F F F F F F F F
F F ˂
– F ˆ F www.schoolDD.com 3
5. F F
F
F
F
F
F F m F F F
Q= F (J)
Q = mL m= (kg)
L= F (J/kg)
F F
Lm (J/kg) ˈ Lv (J/kg)
333x103 2256x103
58.6x103 452x103
5.23x103 20.9x103
F 2 F F 200 -10˚ C ˈ
F ˈ F 190 ( c = 2100 J/kg K, c =
3 3
4186 J/kg K, Lm = 333x10 J/kg, Lv = 2256x10 J/kg )
“ F F ˈ
F F F F ˇ F F ”
Q1 Q2 Q3 Q4
200 g 200 g 200 g 200 g 190 g + 10 g
-10° C 0° C 0° C 100° C 100° C
– F ˆ F www.schoolDD.com 4
6. F F 200 g -10° C ˈ 0° C
Q1 = mc∆T
= 0.2x2100x(0-(-10))
Q1 = 4200 J
F F 200 g 0° C ˈ 0° C
Q2 = mL
= 0.2x333x103
Q2 = 66600 J
F F 200 g 0° C ˈ 100° C
Q3 = mc∆T
= 0.2x4186x(100-0)
Q3 = 83720 J
F F 10 g 100° C ˈ 10 g 100° C
Q4 = mL
= 0.01x2256x103
Q4 = 22560 J
F Q = Q1 + Q2 + Q3 + Q4
= 4200 + 66600 + 83720 + 22560
Q = 177080 J Ans
F 3
100 100˚ C F F F ˈ
90˚ C (c = 4186 J/kg K, Lv = 2256x103 J/kg)
“ F
”
Q1 Q2
100 g 100 g 100 g
100° C 100° C 90° C
F 100 g 100° C F ˈ 100 g 100° C
Q1 = mLv
= 0.1x2256x103 (L =L F )
Q1 = 225600 J
F 100 g 100° C ˈ 100 g 90° C
Q2 = mc∆T
= 0.1x4186x(100-90)
Q2 = 4186 J
F F Q = Q1 + Q2
= 225600 + 4186
Q = 229786 J Ans
– F ˆ F www.schoolDD.com 5
7. F 4
F F 1 20 ˚C F ˈ -10 ˚C F
F F (c = 2100 J/kg K, c = 4186 J/kg K, Lm = 333x103 J/kg)
“ F
”
Q1 Q2 Q3
1 kg 1 kg 1 kg 1 kg
20° C 0° C
0° C -10° C
F 1 kg 20° C ˈ 1 kg 0° C
Q1 = mc∆T
= 1.0x4186x(20-0)
Q1 = 83720 J
F 1 kg 0° C ˈ 1 kg 0° C
Q2 = mLm
= 1.0x333x103 (L =L )
Q2 = 333000 J
F 1 kg 0° C ˈ 1 kg -10° C
Q3 = mc∆T
= 1.0x2100x(0-(-10))
Q3 = 21000 J
F F Q = Q1 + Q2 + Q3
= 83720 + 333000 + 21000
Q = 437720 J Ans
10.1.6 F
F F F F
F F F F
F F F F
F = F F
Q =Q Q = Q
F 5
F 200 FF 300˚ C F 1 20
˚C F F ˈ F ( c = 500 J/kg K, c = 4200 J/kg )
– F ˆ F www.schoolDD.com 6
8. 0.2 kg 0.2 kg
Q Q
300° C t° C t ≤ 100° C F ˈ
t = 300° C F
1 kg 1 kg
100° C ˈ F
Q 20° C Q t° C
Q =Q
(mc∆T) = (mc∆T)
F F ˈ t° C 20 < t ≤100
F F 0.2x500x(300- t) = 1.0x4200x(t-20)
30000 - 100 t = 4200t – 84000
114000 = 4300t
t = 26.5° C Ans ( )
F 6
F 5 F F ˈ 2 ˈ 0.5
F ˈ F
2 kg 2 kg
Q Q
300° C t° C t ≤ 100° C F ˈ
t = 300° C F
0.5 kg 0.5 kg
Q 100° C ˈ F
Q 20° C t° C
Q =Q
(mc∆T) = (mc∆T)
F F ˈ t° C 20 < t ≤100
F F 2.0x500x(300- t) = 0.5x4200x(t-20)
30000 - 100 t = 2100t – 42000
342000 = 3100t
t = 110.3° C > 100° C F ˈ F ˈ
F ˈ 100° C F F
2 kg 2 kg
Q Q 100° C
300° C
0.5 kg 0.5 kg +
Q 20° C Q 1 100° C Q 2
100° C
– F ˆ F www.schoolDD.com 7
9. ˈ F F
Q =Q
(mc∆T) = (mc∆T) 1 + (mL) 2
F F 2.0x500x(300-100) = 0.5x4200x(100-20) + mx2256x103
32000 = 2256x103
m = 0.014 kg
ˈ 0.014 kg 100° C F F 0.5 0.014 = 0.486 kg 100° C Ans
F 7
˄ 1 2 20˚ C F FF 1
200 ˚C F ˈ F ( c = 1000 J/kg K, c
= 4200 J/kg c = 400 J/kg K )
1 kg 1 kg
Q 200° C
Q t° C
˄ 1 kg ˄ 1 kg
t° C 20 < t ≤ 100° C F ˈ
20° C Q ˁ
Q
2 kg 2 kg
20° C Q t° C
Q =Q
(mc∆T) = (mc∆T) ˄ + (mc∆T)
F F ˈ t° C 20 < t ≤100
F F 1.0x400x(200- t) = 1.0x1000x(t-20) + 2.0x4200x(t-20)
80000 - 400 t = 1000t – 20000 + 8400 t - 168000
268000 = 9800t
t = 27.35° C Ans ( )
F 8
F 200 1 30 ˚C F 100
0 ˚C F ( c F = 800 J/kg K, c = 4200 J/kg K,
L = 333x103 J/kg )
– F ˆ F www.schoolDD.com 8
10. 1 kg 1 kg
30° C Q t° C
Q
F 0.2 kg F 0.2 kg 0 < t < 30° C
30° C Q F
t° C
0.1 kg 0.1 kg
0.1 kg
Q Q 0° C Q t° C
0° C
Q =Q
(mc∆T) + (mc∆T) F = (mL) + (mc∆T)
F F ˈ t° C 0 < t < 30
F F 1.0x4200x(30- t) + 0.2x800x(30- t) = 0.1x333x103 + 0.1x4200x(t-0)
4360x(30- t) = 33300 + 420t
97500 = 4780t
t = 20.4° C Ans ( )
F 9
F 1 100 ˚C F 200 F
ˈ F ( c = 500 J/kg K, c = 4200 J/kg K, L = 333x103 J/kg )
1 kg 1 kg
Q 100° C Q t° C
0 < t < 100° C
0.2 kg 0.2 kg
0.2 kg
Q Q 0° C
Q t° C
0° C
Q =Q
(mc∆T) = (mL) + (mc∆T)
F F ˈ t° C 0 < t < 100
3
F F 1.0x500x(100- t) = 0.2x333x10 + 0.2x4200x(t-0)
50000 - 500t = 66600 + 840t
-16600 = 1340t
– F ˆ F www.schoolDD.com 9
11. t = -12.39° C F ˈ F F ˈ 0° C
ˈ F
F F
1 kg 1 kg
Q 100° C Q 0° C
0.2 kg +
Q 0° C
Q 0° C
Q =Q
(mc∆T) = (mL)
F F 1.0x500x(100- 0) = mx333x103
50000 = 333x103m
m = 0.15 kg = 150 g < 200 g OK
F F ˈ 0° C 0.15 kg Ans
10.1.7 F F
3
1. F
- F F F ˈ F F F
F F F
2. F
- F F ˈ F F F
F F F F F F F
FF F F F
3. F F
- F F F F F F F
F ˂
– F ˆ F www.schoolDD.com 10
12. 10.2 F
- F F F F F F
F ˈ F
10.2.1 F
F ʽ F F
P
T
V ן
۾ PV = F 1
V
10.2.2 F
F ʽ F F
V
V ןT
P
= F T
10.2.3 F
F F F
ן
V
= F
۾ ܄ ۾ ܄
F F F
F = 1 2 (T F )
܂ ܂
F F P, V F F = F F F F T
F ˈ K F
– F ˆ F www.schoolDD.com 11
13. F
ןn
୫
F
n= F =
1
۾ ܄ ۾ ܄
= F F F 1 2
F ܖ ܂ ܖ ܂ F (T F )
ˈ F
PV = nRT R= F F = 8.31 J/mol K
. F
n= ۼ
ۯ
= 6.02 x 1023
F 1 F 6.02x1023
F PV =
ۯۼ
RT
ୖ ଼.ଷଵ
F F KB =
ۯۼ
= F F F =
.ଶ୶ଵమయ
= 1.38x10-23 J/K
F PV = NKB T
PV = nRT PV = NKB T F F F F
F ˆ F F F
1. F PV = nRT
ଵ
2. F F F ןT, P ןn, V ןT, V ןn ן F
P P
3. F F F F F 1 2 F F F
F F
భ భ మ మ
= R = R
୬భ భ ୬మ మ
భ భ మ మ
୬భ భ
=
୬మ మ
(P F ˈ P F )
F F
– F ˆ F www.schoolDD.com 12
14. F 10
F 1 F 2 x 105 Pa 7˚ C F F F F
2 F F ˈ F
V 1 = 1 m3 V 2 = 2 m3
P1 = 2x105 Pa P2 = P 1
T1 = 273+7 = 280 K T2 = ?
n1 n2 = n1
F PV = nRT
F F 2
భ భ మ మ
=
୬భ భ ୬మ మ
P n
భ మ
F భ
=
మ
ଵ ଶ
=
ଶ଼ మ
T2 = 560 K 560 273 = 287° C Ans
F 11
F F 105 Pa F 27˚ C ˈ -3˚ C ˈ
F
V1 V2 = V1
P1 = 2x105 Pa P2 = ?
T1 = 273+27= 300 K T2 = 273+(-3) = 270 K
n1 n2 = n1
F PV = nRT
F F 2
భ భ మ మ
=
୬భ భ ୬మ మ
V n
– F ˆ F www.schoolDD.com 13
15. భ మ
F భ
=
మ
ଵఱ మ
=
ଷ ଶ
P2 = 0.9x105 Pa Ans
F 12
F F F 17˚ C F 2 x 105 Pa F
F ˈ 27˚ C F ˈ F (
=105 Pa)
V1 V2 = V1
Pg1 = 2x105 Pa Pg2 = ?
T1 = 273+17= 290 K T2 = 273+27 = 300 K
n1 n2 = n1
F PV = nRT
F F 2
భ భ మ మ
=
୬భ భ ୬మ మ
V n
భ మ
F భ
=
మ
ሺౝశ ౌబ ሻభ ሺౝశ ౌబ ሻమ
భ
=
మ
F P FF ˈ P F F
ଶ୶ଵఱ ାଵఱ ౝమ ାଵఱ
=
ଶଽ ଷ
Pg 2 = 2.09x105 Pa Ans
F 13
F 10 27˚ C 105 Pa F
F
– F ˆ F www.schoolDD.com 14
16. V = 10
P = 105 Pa
T = 273+27 = 300 K
n=?
m=?
F PV = nRT
F F F F
F F 105(10x10-3) = n (8.31)(300) 1 = 1000 cc = 1000 cm3 = 1000(10-6 m3) = 10-3 m3
n = 103/ 2493 = 0.4 Ans
୫
n= m = nM
= 0.4x2.0x10-3
m = 8.0x10-4 kg Ans
F 14
F 50 F 10 27˚ C
F F F F 5 17˚ C F F F
( R = 8.31 J/mol K, MN2 = 28 g/mol, 1 atm = 105 Pa )
V1 = 50x10-3 m3 V2 = 50x10-3 m3
P1 = 10 atm P2 = 5 atm
T1 = 273+27 = 300 K T2 = 273+17 = 290 K
n1 = ? n2 = ?
. n1 F F P1 V1 = n1RT1
10x105x50x10-3 = n1x8.31x300
n1 = 20
. n2 F F P2 V2 = n2RT2
5x10 x50x10-3 = n2x8.31x290
5
n2 = 10.4
F F F n1 n2 = 20 10.4 = 9.6 9.6x28x10-3 = 0.27 kg Ans
– F ˆ F www.schoolDD.com 15
17. F 15
F 64 27˚ C 20 F F
F ( R = 8.31 J/mol K, MO2 = 28 g/mol )
m = 64 g
T = 273+27 = 300 K
V = 20x10-3 m3
P=?
P F F PV = nRT
ସ ୫
Px20x10-3 = ଷଶx8.31x300 n=
P = 2.493x105 Pa Ans
F 16
F 1 1.3 0˚ C 1
13 10 27˚ C
V1 = 1 V2 = 10
m1 = 1.3 g m2 = 13 g
T1 = 273+0 = 273 K T2 = 273+27 = 300 K
P1 = 1 atm P2 = ?
F PV = nRT
F F 2
భ భ మ మ
=
୬భ భ ୬మ మ
୫
F n=
M
భ భ మ మ
F ୫భ భ
=
୫మ మ
ଵ୶ଵ మ ୶ଵ
=
ଵ.ଷ୶ଶଷ ଵଷ୶ଷ
P2 = 1.10 atm Ans
– F ˆ F www.schoolDD.com 16
18. F 17
F F F F
ˈ F
V1 V2 = V1
P1 P2 = ½ P 1
T1 T2 = T1
n1 n2 = ?
F PV = nRT
F F 2
భ భ మ మ
=
୬భ భ ୬మ మ
F V T
భ మ
F ୬భ
=
୬మ
భ
భ
మ భ
=
୬భ ୬మ
n2 = ½ n1 Ans
F 18
F F 10 kg/m3 27˚ C 2 F F
F 17˚ C 1 F F F
V1 V2 = V1
T1 = 273+27 = 300 K T2 = 273+17 = 290 K
P1 = 2 atm P2 = 1 atm
ߩ1 = 10 kg/m3 ߩ2 = ?
F PV = nRT
F F 2
భ భ మ మ
=
୬భ భ ୬మ మ
୫
F n=
M
– F ˆ F www.schoolDD.com 17
19. భ భ మ మ
F ୫భ భ
=
୫మ మ
భ మ
ౣభ = ౣమ
భ భ మ మ
భ మ
=
ఘభ భ ఘమ మ
ଶ ଵ
=
ଵ୶ଷ ఘమ ୶ଶଽ
ߩ ଶ = 5.17 kg/m3 Ans
10.3 F F
10.3.1 F
F
1. F F F ˈ
F F F
2. F F ˈ F
3. F ˈ F F F
10.3.2 F ( < EK > )
F F < EK > ˈ F F
1 F ˈ (J)
< EK > = KB T
F F N F N< EK >
ଷ
N< EK > = ଶ NKB T
ଷ
= ଶ PV ( PV = NKB T )
ଷ
= ଶ nRT ( PV = nRT )
- < EK > F F F F F
– F ˆ F www.schoolDD.com 18
20. 10.3.3 F
F F F vrms (vroot mean square )
F ˈ F (m/s)
܂܀
vrms = ට M= F 1 (kg)
ۻ
- vrms F T M
- vrms F F (v) F F F
F 19
F 20 27˚ C ( R = 8.31 J/mol K, MH2 = 2 g/mol )
. F F
. F F
. vrms F
m = 20 g
T = 273+27 = 300 K
. < EK > = ?
ଷ ୖ ଼.ଷଵ
< EK > = KB T KB = = = 1.38x10-23
ଶ ఽ .ଶ୶ଵమయ
ଷ
= x 1.38x10-23x300
ଶ
< EK > = 6.21x10-25 J Ans
. N< EK > = ?
. N N = n NA
୫ ଶ
= = x 6.02x1023
ଶ
N = 6.02x1024
N< EK > = 6.02x1024x 6.21x10-25 = 3.73 J Ans
– F ˆ F www.schoolDD.com 19
21. . vrms = ?
ଷୖ
vrms = ට
ଷ୶଼.ଷଵ୶ଷ
= ට = √3739500
ଶ௫ଵషయ
vrms = 1933.78 m/s Ans
F 20
F F F 3 10 2 Pa
n=3
V = 10 = 10x10-3 m3
P = 2 Pa
N<EK> = ?
<EK> = ?
. N N = n NA = 3x6.02x1023
ଷ ଷ
F F N< EK > = ଶ
NKBT = ଶ
PV ( PV = NKBT)
ଷ -3
= x2x10x10
ଶ
N< EK > = 3x10-2 J Ans
ଷ୶ଵషమ ଷ୶ଵషమ
F < EK > < EK > =
=
ଷ୶.ଶ୶ଵమయ
< EK > = 1.66x10-26 J Ans
F 21
F F 2x 1025 F F 105 Pa
F F
N/V = 2x1025 /m3
P = 1x105 Pa
<EK> = ?
ଷ
F < EK > < EK > =
ଶ
KBT
ଷ ଷ
F N< EK > = ଶ
NKBT =
ଶ
PV ( PV = NKBT)
ଷ
< EK > = ଶ
ଷ ଵ୶ଵఱ
= ଶ x ଶ୶ଵమఱ
< EK > = 7.5x10-21 J Ans
– F ˆ F www.schoolDD.com 20
22. F 22
F
. F F ˈ 2 F F ˈ F
. F F ˈ 2 F F ˈ F
.
T1 T2 = 2 T1
<EK1> <EK2> = ?
ଷ
< EK > = ଶ
KBT
F < EK > ןT
ழாేభ வ భ భ
= =
ழாేమ வ మ ଶభ
< EK2 > = 2< EK1 > Ans
.
V1 V2 = V1
P1 P2 = 2 P 1
N1 N2 = N1
<EK1> <EK2> = ?
ଷ
< EK > = ଶ
KBT
ଷ ଷ
N< EK > = ଶ
NKBT =
ଶ
PV
F < EK > ןP N V
ழாేభ வ భ భ
= =
ழாేమ வ మ ଶభ
< EK2 > = 2< EK1 > Ans
F 23
F A 1 7˚ C F B 2 27˚ C
F F ˈ F ( R = 8.31 J/mol K )
nA = 1 nB = 2
A TA = 273 + 7 = 280 K + B TB = 273 + 27 = 300 K
<EKA> <EKB>
– F ˆ F www.schoolDD.com 21
23. ଷ
N< EK > N< EK > = NKBT
ଶ
ଷ
= nRT
ଶ
ଷ ଷ
(N< EK >)A + (N< EK >)B = (ଶ nRT)A + (ଶ nRT)B
ଷ
= R(nATA + nBTB)
ଶ
ଷ
= x8.31(1x280 + 2x300)
ଶ
F = 1.097x104 J Ans
F 24
F ˈ F F ( MH2 = 2 g/mol, MO2 =
32 g/mol)
H2
vrmsH2 O2
vrmsO2
ଷୖ
vrms = ට
ଵ
F vrms ן T
√
୴౨ౣ౩ౄమ ଷଶ
୴౨ౣ౩ోమ
= ටోమ = ට = 4
ౄమ ଶ
vrmsH2 = 4 vrmsO2 Ans
F 25
F ʽ F F ˈ 4 F
vrms ˈ F
ߩଵ ߩଶ = 4ߩଵ
vrms1 vrms2
ଷୖ
vrms = ට
PV = nRT
F RT = ୬
ଷ
vrms = ට ୬
– F ˆ F www.schoolDD.com 22
24. ଷ ୬ ୫
= ටఘ = = ߩ
ଵ
F vrms ן P
ඥఘ
୴౨ౣ౩భ ఘ ସఘ
= ටఘమ = ටఘభ = 2
୴౨ౣ౩మ భ భ
vrms2 = 2 vrms1 Ans
10.4
-
- F FF F F
F U F F
F F ˈ F F F
F F F F F F F
F F
U = N< EK >
ଷ
F FF U = ଶ
NKBT
ଷ
= nRT
ଶ
ଷ
= ଶ
PV
10.4.1 F 1 F F
F F F F
〉 ∆W
∆Q = ∆U + ∆W
〉 ∆U
〉 ∆Q
ΔW = FΔs
= PAΔs
= PΔV
– F ˆ F www.schoolDD.com 23
25. F F F +
∆Q
F -
+
∆U
-
+
∆W
F -
F 26
F F F 1000 J F F F 200 J F
F F F
∆W = ?
〉 ∆U = 200 J
〉 ∆Q = 1000 J
∆Q = ∆U + ∆W
1000 = 200 + ∆W
∆W = 800
F F = 800 J ( ∆W ˈ + ) Ans
F 27
F 1024 F F F F 1˚ C F F F F F F
(KB = 1.38x10-23 )
N = 1024
∆T = 1
∆V = 0
〉 ∆Q = ?
∆Q = ∆U + ∆W
ଷ
= NKB∆T + P∆V
ଶ
ଷ
= x1024x1.38x10-23x1 + 0
ଶ
∆Q = 20.7
F F F F F ∆Q = 20.7 J Ans (∆Q ˈ +)
– F ˆ F www.schoolDD.com 24
26. F 28
100 N F 1 F 1K
F F F F 20 cm. ( R = 8.31 J/mol K )
F = 100 N
n=1
∆T = 1 K
0.20 ∆Q = ?
∆Q = ∆U + ∆W
ଷ
= ଶ
nR∆T + (-F∆s) ( F ˈ )
ଷ
= x1x8.31x1 – 100x0.20
ଶ
∆Q = -7.5 ( ˈ F )
F ∆Q = 7.5 J Ans
F 29
F F F F F F F
P
∆W
∆U ∆V
〉 ∆Q = ?
∆Q = ∆U + ∆W
ଷ
= ଶ
NKB∆T + P∆V
ଷ
= P∆V + P∆V ( PV = NKBT)
ଶ
ହ
∆Q = P∆V
ଶ
F F F F F ∆Q =
ହ
ଶ
P∆V J Ans
– F ˆ F www.schoolDD.com 25
27. F 30
F F F 20 27˚ C 105 Pa F
ˈ 57˚ C F F F F F F
V1 = 20
T1 = 273 + 27 = 300 K V2 = ?
∆W T2 = 273 + 57 = 330 K
P1 = 105 Pa
∆U P2 = P1
〉 ∆Q = ?
భ భ మ మ
V2 F ୬భ భ
=
୬మ మ
P n
భ మ
F భ
=
మ
ଶ మ
=
ଷ ଷଷ
V2 = 22
∆Q = ∆U + ∆W
ଷ
= NKB∆T + P∆V
ଶ
ଷ
=
ଶ
P∆V + P∆V ( PV = NKBT)
ହ ହ
= P∆V = x10 x(22-2)x10-3
5
ଶ ଶ
∆Q = 500
F F F F F ∆Q = 500 J Ans
– F ˆ F www.schoolDD.com 26
