AP Physics
Thermodynamics
Thermodynamics Problem Set
1. A swimmer does 6.7  105 J of work and gives off 41
.  105 J of heat during a workout.
Determine U , W , and Q for the swimmer.
2. Three different processes act on a system. (a) In process A, 42 J of work are done
on the system and 77 J of heat are added to the system. Find the change in the
system’s internal energy. (b) In process B, the system does 42 J of work and 77 J
of heat are added to the system. What is the change in the system’s internal
energy? (c) In process C, the system’s internal energy decreases by 120 J while the
system performs 120 J of work on its surroundings. How much heat was added to
the system?
3. A basketball player does 213
.  105 J of work during her time in the game, and
evaporates 0.110 kg of water. Assuming a latent heat of 2.26  106 J / kg for the
4.
perspiration (the same as for water) determine (a) the change in the player’s
internal energy and (b) the number of nutritional calories the player has converted
to work and heat.
An ideal gas is compressed at constant pressure to one-half its initial volume. If the
pressure of the gas is 120 kPa, and 760 J of work is done on it, find the initial
volume of the gas.
5. As an ideal gas expands at constant pressure from a volume of 0.74 m3 to a volume
6.
of 2.3 m3 it does 93 J of work. What is the gas pressure during this process?
Find the work done by a monatomic ideal gas as it expands from point A to point C
along the path shown in Figure 18–23. (b) If the temperature of the gas is 220 K at
point A, what is its temperature at point C? (c) How much heat has been added to or
removed from the gas during this process?
7. (a) Three moles of an ideal monatomic gas expand isothermally at a temperature of
21 °C. If the volume of the gas quadruples during this process, what is (a) the work
done by the gas and (b) the heat flow into the gas?
8. One mole of an ideal gas is taken through the cycle ABCA shown in the PV diagram.
State A has volume of 0.0135 m3 and pressure 1.5 x 105 Pa, and state C has volume
0.0518 m3. Process CA lies along the 244+1K isotherm. The molar heat capacity
(specific heat) for the gas is 20.8 J/(mol*K).
a. What is the temperature at state B?
b. Determine the heat Qab added to the gas during the process AB.
c. Determine the change ∆Uab = Ub – Ua in the internal energy.
d. Determine the work Wbc done by the gas on its surroundings during the process
BC.
e. The net heat added to the gas for the entire cycle is 3020 J. Determine the net
work done by the gas on its surroundings during the cycle.
f. Determine the efficiency of a Carnot engine that operates between the
maximum and minimum temperatures in the cycle.
1.
Q  4.1105 J
W  6.7 105 J
U  Q  W  4.1105 J  6.7 105 J  10.8 105 J
2. (a) U  Q  W  77 J  (42 J)  119 J
(b) U  Q  W  77 J  42 J  35 J
(c)
Q  U  W  120 J  120 J  0

J 
5
(a) U  Q  W  mL  W  (0.110 kg)  2.26 106
  2.13 10 J  –462 kJ
kg 

3.
 0.2389 cal 
(4.62  105 J) 
  110 kcal
1J


(b)
4.
PV  W
P (Vf  Vi )  W
V

P  i  Vi   W
2

2W
Vi 
P
2(760 J)

120  103 Pa
 1.3  102 m3
P (Vf  Vi )  W
5.
P

W
Vf  Vi
93 J
2.3 m  0.74 m3
3
 60 Pa
6.
(a) WAC   PV  area under P-V curve from A to C  Arect  Atri,1  Atri,2  Asquare
Arect  lw  (10 m  2 m3 )(200 kPa)  1600 kJ
1
1
Atri,1  bh  (6 m3  4 m3 )(600 kPa – 200 kPa)  400 kJ
2
2
1
1
Atri,2  bh  (8 m3  6 m3 )(600 kPa – 400 kPa)  200 kJ
2
2
Asquare  wh  (8 m3  6 m3 )(400 kPa – 200 kPa)  400 kJ
WAC  1600 kJ  400 kJ  200 kJ  400 kJ  2.6 MJ
(b)
Vi Vf

Ti Tf
V
Tf  f Ti
Vi

10 m3
2 m3
(220 K)
 1100 K
 Vf 
 4Vi
J 

7. (a) W  nRT ln    (3 mol)  8.31
 (273.15 K  21 K)ln 
mol  K 

 Vi 
 Vi
(b)
Q  U  W  0  10 kJ  10 kJ

  10 kJ
