This document discusses concepts related to the gas laws including: 1. Definitions of key terms like pressure, volume, temperature, moles, and the gas constant R. 2. Equations relating these variables like the ideal gas law PV=nRT and how pressure, volume, and temperature are directly proportional while temperature and moles are directly proportional. 3. Explanations of how the gas laws can be used to calculate heat, work, internal energy, and other thermodynamic properties of gases.

1. 10
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2. – F ˆ F www.schoolDD.com 1
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 F F F F F ( ˈ F
SI)
F
C =
R = F
F = F
K =
100
F F
0
° CK
373.16
273.16
K = C + 273
۱
૞
=
‫܀‬
૝
=
۴ି૜૛
ૢ

3. – F ˆ F www.schoolDD.com 2
10.1.2 F
1. F ( C ) F F
ˈ F F ˈ F (J/K)
2. F ( c ) F F 1 F
ˈ F F ˈ F (J/kg K)
F F F F F m ΔT F F
Q = F (J)
m = (kg)
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)
(-10˚C 0˚C)
4186
2100
900
450
390
140
130
m
∆Q
〉 ∆T
C =
ઢ‫ۿ‬
ઢ‫܂‬
m
∆Q
〉 ∆T
c =
ઢ‫ۿ‬
‫ܕ‬ઢ‫܂‬
Q = mc∆T

4. – F ˆ F www.schoolDD.com 3
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
- 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 ˂
s

5. – F ˆ F www.schoolDD.com 4
F F
F F m F F F
Q = F (J)
m = (kg)
L = F (J/kg)
F
Lm (J/kg)
F
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 =
4186 J/kg K, Lm = 333x103
J/kg, Lv = 2256x103
J/kg )
“ F F ˈ
F F F F ˇ F F ”
F
F
F
F
Q = mL
200 g
-10° C
Q1
200 g
0° C
200 g
0° C
200 g
100° C
190 g + 10 g
100° C
Q2 Q3 Q4

6. – F ˆ F www.schoolDD.com 5
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 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
100 g
100° C
100 g
100° C
Q1
100 g
90° C
Q2
“ F”

7. – F ˆ F www.schoolDD.com 6
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 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
F 5
F 200 F F 300˚ C F 1 20
˚C F F ˈ F ( c = 500 J/kg K, c = 4200 J/kg )
1 kg
20° C
1 kg
0° C
Q1
1 kg
0° C
Q3
1 kg
-10° C
Q2
Q = Q Q = Q
“ F”

8. – F ˆ F www.schoolDD.com 7
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
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
1 kg
20° C Q
1 kg
t° CQ
0.2 kg
300° C
Q
0.2 kg
t° CQ t ≤ 100° C F ˈ
t = 300° C F
100° C ˈ F
0.5 kg
20° C Q
0.5 kg
t° CQ
2 kg
300° C
Q
2 kg
t° CQ t ≤ 100° C F ˈ
t = 300° C F
100° C ˈ F
0.5 kg
20° C Q 1
0.5 kg
100° C
Q
2 kg
300° C
Q
2 kg
100° CQ
+
100° CQ 2

9. – F ˆ F www.schoolDD.com 8
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 F F 1
200 ˚C F ˈ F ( c = 1000 J/kg K, c
= 4200 J/kg c = 400 J/kg K )
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 )
2 kg
20° C Q
2 kg
t° C
Q
1kg
200° C
Q
1kg
t° CQ
20 < t ≤ 100° C F ˈ
˄ 1 kg
20° C
˄ 1 kg
t° CQ ˁ

10. – F ˆ F www.schoolDD.com 9
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 )
Q = Q
(mc∆T) = (mL) + (mc∆T)
F F ˈ t° C 0 < t < 100
F F 1.0x500x(100- t) = 0.2x333x103
+ 0.2x4200x(t-0)
50000 - 500t = 66600 + 840t
-16600 = 1340t
1 kg
30° C Q
1 kg
t° C
Q
0.1 kg
0° C
Q
0.1 kg
0° C
Q 0 < t < 30° C
F 0.2 kg
30° C
F 0.2 kg
t° CQ F
Q
0.1 kg
t° C
1 kg
100° C Q
1 kg
t° C
Q
0.2 kg
0° C
Q
0.2 kg
0° C
Q
0 < t < 100° C
Q
0.2 kg
t° C

11. – F ˆ F www.schoolDD.com 10
‫׵‬ t = -12.39° C F ˈ F F ˈ 0° C
ˈ F
F F
Q = Q
(mc∆T) = (mL)
F F 1.0x500x(100- 0) = mx333x103
50000 = 333x103
m
‫׵‬ 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
F F F F F
3. F F
- F F F F F F F
F ˂
1 kg
100° C Q
1 kg
0° C
Q
0.2 kg
0° C
Q
+
0° C
Q

12. – F ˆ F www.schoolDD.com 11
10.2 F
- F F F F F F
F ˈ F
10.2.1 F
F ʽ F F
10.2.2 F
F ʽ F F
10.2.3 F
F F F
V ‫ן‬
୘
୔
୔୚
୘
= F
F
V ‫ן‬
૚
‫۾‬
P
1
V
T
PV = F
V ‫ן‬ T
V
T
P
୚
୘
= F
‫۾‬૚‫܄‬૚
‫܂‬૚
=
‫۾‬૛‫܄‬૛
‫܂‬૛
F F F
1 2 (T F )
F F P, V F F = F F F F T
F ˈ K F

13. – F ˆ F www.schoolDD.com 12
F
୔୚
୘
‫ן‬ n n = F =
୫
୑
F
n =
୒
‫ۼ‬‫ۯ‬
F 1 F 6.02x1023
F PV =
୒
‫ۼ‬‫ۯ‬
RT
F F KB =
ୖ
‫ۼ‬‫ۯ‬
= F F F =
଼.ଷଵ
଺.଴ଶ୶ଵ଴మయ
= 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
2. F F F P ‫ן‬ T, P ‫ן‬ n, V ‫ן‬ T, V ‫ן‬ n P ‫ן‬
ଵ
୚
F
3. F F F F F 1 2 F F F
F F
୔భ୚భ
୬భ୘భ
= R
୔మ୚మ
୬మ୘మ
= R
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
(P F ˈ P F )
F F
PV = nRT
ˈ F
R = F F = 8.31 J/mol K
. F
= 6.02 x 1023
F
1
‫۾‬૚‫܄‬૚
‫ܖ‬૚‫܂‬૚
=
‫۾‬૛‫܄‬૛
‫ܖ‬૛‫܂‬૛
F F F 1 2
F (T F )

14. – F ˆ F www.schoolDD.com 13
F 10
F 1 F 2 x 105
Pa 7˚ C F F F F
2 F F ˈ F
F PV = nRT
F F 2
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
P n
F
୚భ
୘భ
=
୚మ
୘మ
ଵ
ଶ଼଴
=
ଶ
୘మ
‫׵‬ T2 = 560 K 560 273 = 287° C Ans
F 11
F F 105
Pa F 27˚ C ˈ -3˚ C ˈ
F
F PV = nRT
F F 2
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
V n
V1 = 1 m3
P1 = 2x105
Pa
T1 = 273+7 = 280 K
n1
V2 = 2 m3
P2 = P1
T2 = ?
n2 = n1
V1
P1 = 2x105
Pa
T1 = 273+27= 300 K
n1
V2 = V1
P2 = ?
T2 = 273+(-3) = 270 K
n2 = n1

15. – F ˆ F www.schoolDD.com 14
F
୔భ
୘భ
=
୔మ
୘మ
ଵ଴ఱ
ଷ଴଴
=
୔మ
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)
F PV = nRT
F F 2
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
V n
F
୔భ
୘భ
=
୔మ
୘మ
ሺ୔ౝశ ౌబሻభ
୘భ
=
ሺ୔ౝశ ౌబሻమ
୘మ
F P F F ˈ P F F
ଶ୶ଵ଴ఱାଵ଴ఱ
ଶଽ଴
=
୔ౝమାଵ଴ఱ
ଷ଴଴
‫׵‬ Pg 2 = 2.09x105
Pa Ans
F 13
F 10 27˚ C 105
Pa F
F
V1
Pg1 = 2x105
Pa
T1 = 273+17= 290 K
n1
V2 = V1
Pg2 = ?
T2 = 273+27 = 300 K
n2 = n1

16. – F ˆ F www.schoolDD.com 15
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
n =
୫
୑
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 )
. n1 F F P1 V1 = n1RT1
10x105
x50x10-3
= n1x8.31x300
n1 = 20
. n2 F F P2 V2 = n2RT2
5x105
x50x10-3
= n2x8.31x290
n2 = 10.4
‫׵‬ F F F n1 n2 = 20 10.4 = 9.6 9.6x28x10-3
= 0.27 kg Ans
V = 10
P = 105
Pa
T = 273+27 = 300 K
n = ?
m = ?
V1 = 50x10-3
m3
P1 = 10 atm
T1 = 273+27 = 300 K
n1 = ?
V2 = 50x10-3
m3
P2 = 5 atm
T2 = 273+17 = 290 K
n2 = ?

17. – F ˆ F www.schoolDD.com 16
F 15
F 64 27˚ C 20 F F
F ( R = 8.31 J/mol K, MO2 = 28 g/mol )
P F F PV = nRT
Px20x10-3
=
଺ସ
ଷଶ
x8.31x300 n =
୫
୑
‫׵‬ P = 2.493x105
Pa Ans
F 16
F 1 1.3 0˚ C 1
13 10 27˚ C
F PV = nRT
F F 2
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
F n =
୫
୑
M
F
୔భ୚భ
୫భ୘భ
=
୔మ୚మ
୫మ୘మ
ଵ୶ଵ
ଵ.ଷ୶ଶ଻ଷ
=
୔మ୶ଵ଴
ଵଷ୶ଷ଴଴
‫׵‬ P2 = 1.10 atm Ans
m = 64 g
T = 273+27 = 300 K
V = 20x10-3
m3
P = ?
V1 = 1
m1 = 1.3 g
T1 = 273+0 = 273 K
P1 = 1 atm
V2 = 10
m2 = 13 g
T2 = 273+27 = 300 K
P2 = ?

18. – F ˆ F www.schoolDD.com 17
F 17
F F F F
ˈ F
F PV = nRT
F F 2
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
F V T
F
୔భ
୬భ
=
୔మ
୬మ
୔భ
୬భ
=
భ
మ
୔భ
୬మ
‫׵‬ n2 = ½ n1 Ans
F 18
F F 10 kg/m3
27˚ C 2 F F
F 17˚ C 1 F F F
F PV = nRT
F F 2
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
F n =
୫
୑
M
V1
P1
T1
n1
V2 = V1
P2 = ½ P1
T2 = T1
n2 = ?
V1
T1 = 273+27 = 300 K
P1 = 2 atm
ߩ1 = 10 kg/m3
V2 = V1
T2 = 273+17 = 290 K
P2 = 1 atm
ߩ2 = ?

19. – F ˆ F www.schoolDD.com 18
F
୔భ୚భ
୫భ୘భ
=
୔మ୚మ
୫మ୘మ
୔భ
ౣభ
౒భ
୘భ
=
୔మ
ౣమ
౒మ
୘మ
୔భ
ఘభ୘భ
=
୔మ
ఘమ୘మ
ଶ
ଵ଴୶ଷ଴଴
=
ଵ
ఘమ୶ଶଽ଴
‫׵‬ ߩଶ = 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)
F F N F N< EK >
N< EK > =
ଷ
ଶ
NKB T
=
ଷ
ଶ
PV ( PV = NKB T )
=
ଷ
ଶ
nRT ( PV = nRT )
- < EK > F F F F F
< EK > = ૜
૛
KB T

20. – F ˆ F www.schoolDD.com 19
10.3.3 F
F F F vrms (vroot mean square )
F ˈ F (m/s)
- 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
. < EK > = ?
< EK > =
ଷ
ଶ
KB T KB =
ୖ
୒ఽ
=
଼.ଷଵ
଺.଴ଶ୶ଵ଴మయ
= 1.38x10-23
=
ଷ
ଶ
x 1.38x10-23
x300
‫׵‬ < EK > = 6.21x10-25
J Ans
. N< EK > = ?
. N N = n NA
=
୫
୑
=
ଶ଴
ଶ
x 6.02x1023
N = 6.02x1024
‫׵‬ N< EK > = 6.02x1024
x 6.21x10-25
= 3.73 J Ans
vrms = ට
૜‫܂܀‬
‫ۻ‬
M = F 1 (kg)
m = 20 g
T = 273+27 = 300 K

21. – F ˆ F www.schoolDD.com 20
. vrms = ?
vrms = ට
ଷୖ୘
୑
= ට
ଷ୶଼.ଷଵ୶ଷ଴଴
ଶ௫ଵ଴షయ
= √3739500
‫׵‬ vrms = 1933.78 m/s Ans
F 20
F F F 3 10 2 Pa
. N N = n NA = 3x6.02x1023
F F N< EK > =
ଷ
ଶ
NKBT =
ଷ
ଶ
PV (‫׶‬ PV = NKBT)
=
ଷ
ଶ
x2x10x10-3
‫׵‬ N< EK > = 3x10-2
J Ans
F < EK > < EK > =
ଷ୶ଵ଴షమ
୒
=
ଷ୶ଵ଴షమ
ଷ୶଺.଴ଶ୶ଵ଴మయ
‫׵‬ < EK > = 1.66x10-26
J Ans
F 21
F F 2x 1025
F F 105
Pa
F F
F < EK > < EK > =
ଷ
ଶ
KBT
F N< EK > = ଷ
ଶ
NKBT =
ଷ
ଶ
PV (‫׶‬ PV = NKBT)
< EK > = ଷ
ଶ
୔୚
୒
= ଷ
ଶ
x
ଵ୶ଵ଴ఱ
ଶ୶ଵ଴మఱ
‫׵‬ < EK > = 7.5x10-21
J Ans
n = 3
V = 10 = 10x10-3
m3
P = 2 Pa
N<EK> = ?
<EK> = ?
N/V = 2x1025
/m3
P = 1x105
Pa
<EK> = ?

22. – F ˆ F www.schoolDD.com 21
F 22
F
. F F ˈ 2 F F ˈ F
. F F ˈ 2 F F ˈ F
.
< EK > =
ଷ
ଶ
KBT
F < EK > ‫ן‬ T
ழாేభவ
ழாేమவ
=
୘భ
୘మ
=
୘భ
ଶ୘భ
‫׵‬ < EK2 > = 2< EK1 > Ans
.
< EK > =
ଷ
ଶ
KBT
N< EK > = ଷ
ଶ
NKBT =
ଷ
ଶ
PV
F < EK > ‫ן‬ P N V
ழாేభவ
ழாేమவ
=
୔భ
୔మ
=
୔భ
ଶ୔భ
‫׵‬ < 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 )
T1
<EK1>
T2 = 2 T1
<EK2> = ?
V1
P1
N1
<EK1>
V2 = V1
P2 = 2 P1
N2 = N1
<EK2> = ?
A
nA = 1
TA = 273 + 7 = 280 K
<EKA>
B
nB = 2
TB = 273 + 27 = 300 K
<EKB>
+

23. – F ˆ F www.schoolDD.com 22
N< EK > N< EK > =
ଷ
ଶ
NKBT
=
ଷ
ଶ
nRT
(N< EK >)A + (N< EK >)B = (
ଷ
ଶ
nRT)A + (
ଷ
ଶ
nRT)B
=
ଷ
ଶ
R(nATA + nBTB)
=
ଷ
ଶ
x8.31(1x280 + 2x300)
‫׵‬ F = 1.097x104
J Ans
F 24
F ˈ F F ( MH2 = 2 g/mol, MO2 =
32 g/mol)
vrms = ට
ଷୖ୘
୑
F vrms ‫ן‬
ଵ
√୑
T
୴౨ౣ౩ౄమ
୴౨ౣ౩ోమ
= ට
୑ోమ
୑ౄమ
= ට
ଷଶ
ଶ
= 4
‫׵‬ vrmsH2 = 4 vrmsO2 Ans
F 25
F ʽ F F ˈ 4 F
vrms ˈ F
vrms = ට
ଷୖ୘
୑
PV = nRT
F RT =
୔୚
୬
vrms = ට
ଷ୔୚
୬୑
H2
vrmsH2 O2
vrmsO2
ߩଵ
vrms1
ߩଶ = 4ߩଵ
vrms2

24. – F ˆ F www.schoolDD.com 23
= ට
ଷ୔
ఘ
୬୑
୚
=
୫
୚
= ߩ
F vrms ‫ן‬
ଵ
ඥఘ
P
୴౨ౣ౩భ
୴౨ౣ౩మ
= ට
ఘమ
ఘభ
= ට
ସఘభ
ఘభ
= 2
‫׵‬ vrms2 = 2 vrms1 Ans
10.4
-
- F F F F F
F U F F
F F ˈ F F F
F F F F F F F
F F
F F F U =
ଷ
ଶ
NKBT
=
ଷ
ଶ
nRT
=
ଷ
ଶ
PV
10.4.1 F 1 F F
F F F F
U = N< EK >
〉 ∆Q
〉 ∆U
〉 ∆W
∆Q = ∆U + ∆W
ΔW = FΔs
= PAΔs
= PΔV

25. – F ˆ F www.schoolDD.com 24
∆Q
F F F +
F -
∆U
+
-
∆W
+
F -
F 26
F F F 1000 J F F F 200 J F
F F F
∆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
)
∆Q = ∆U + ∆W
=
ଷ
ଶ
NKB∆T + P∆V
=
ଷ
ଶ
x1024
x1.38x10-23
x1 + 0
∆Q = 20.7
‫׵‬ F F F F F ∆Q = 20.7 J Ans (∆Q ˈ + )
〉 ∆Q = 1000 J
〉 ∆U = 200 J
∆W = ?
〉 ∆Q = ?
N = 1024
∆T = 1
∆V = 0

26. – F ˆ F www.schoolDD.com 25
F 28
100 N F 1 F 1 K
F F F F 20 cm. ( R = 8.31 J/mol K )
∆Q = ∆U + ∆W
=
ଷ
ଶ
nR∆T + (-F∆s) ( F ˈ )
=
ଷ
ଶ
x1x8.31x1 – 100x0.20
∆Q = -7.5 ( ˈ F )
‫׵‬ F ∆Q = 7.5 J Ans
F 29
F F F F F F F
∆Q = ∆U + ∆W
=
ଷ
ଶ
NKB∆T + P∆V
=
ଷ
ଶ
P∆V + P∆V ( ‫׶‬ PV = NKBT)
∆Q =
ହ
ଶ
P∆V
‫׵‬ F F F F F ∆Q = ହ
ଶ
P∆V J Ans
n = 1
∆T = 1 K
∆Q = ?
F = 100 N
0.20
〉 ∆Q = ?
P
∆V
∆W
∆U

27. – F ˆ F www.schoolDD.com 26
F 30
F F F 20 27˚ C 105
Pa F
ˈ 57˚ C F F F F F F
V2 F
୔భ୚భ
୬భ୘భ
=
୔మ୚మ
୬మ୘మ
P n
F
୚భ
୘భ
=
୚మ
୘మ
ଶ଴
ଷ଴଴
=
୚మ
ଷଷ଴
V2 = 22
∆Q = ∆U + ∆W
=
ଷ
ଶ
NKB∆T + P∆V
=
ଷ
ଶ
P∆V + P∆V ( ‫׶‬ PV = NKBT)
=
ହ
ଶ
P∆V =
ହ
ଶ
x105
x(22-2)x10-3
∆Q = 500
‫׵‬ F F F F F ∆Q = 500 J Ans
〉 ∆Q = ?
V1 = 20
T1 = 273 + 27 = 300 K
P1 = 105
Pa
V2 = ?
T2 = 273 + 57 = 330 K
P2 = P1
∆W
∆U