A heating element with power output $$P$$ transfers energy to a liquid of mass $$m$$ and specific heat $$c$$. If the liquid's temperature increases from $$T_i$$ to $$T_f$$ with no heat loss, which expression represents the time $$t$$ required?

$$t = \frac{mc(T_f - T_i)}{P}$$

$$t = \frac{P}{mc(T_f - T_i)}$$

$$t = \frac{mcP}{(T_f - T_i)}$$

A block of mass $$M$$ and specific heat $$C_B$$ at temperature $$T_H$$ is placed into a liquid of mass $$m$$ and specific heat $$C_L$$ at temperature $$T_C$$. If the system is isolated, which expression represents the final equilibrium temperature $$T_f$$?

$$T_f = \frac{M C_B T_H + m C_L T_C}{M C_B + m C_L}$$

$$T_f = \frac{M C_B T_H - m C_L T_C}{M C_B - m C_L}$$

$$T_f = \frac{M C_B T_C + m C_L T_H}{M C_B + m C_L}$$

$$T_f = \frac{M C_B T_H + m C_L T_C}{M C_B - m C_L}$$

A resistor of resistance $$R$$ carries a current $$I$$ while immersed in a liquid of mass $$m$$. If the liquid's temperature rises by $$\Delta T$$ in time $$t$$, which expression gives the specific heat $$c$$ of the liquid?

$$c = \frac{I^2 R t}{m \Delta T}$$

$$c = \frac{I R^2 t}{m \Delta T}$$

$$c = \frac{I^2 R}{m t \Delta T}$$

$$c = \frac{I R t}{m \Delta T}$$

A sample of material has density $$\rho$$, volume $$V$$, and specific heat $$c$$. Which expression represents the energy $$Q$$ required to increase its temperature by $$\Delta T$$?

$$Q = \frac{\rho c \Delta T}{V}$$

$$Q = \frac{V c \Delta T}{\rho}$$

Water flows through a heater at a rate of $$R$$ (kg/s). The heater provides power $$P$$. If the water enters at temperature $$T_{in}$$ and has specific heat $$c$$, which expression gives the exit temperature $$T_{out}$$?

$$T_{out} = T_{in} + \frac{P}{R c}$$

$$T_{out} = T_{in} + \frac{R c}{P}$$

$$T_{out} = T_{in} - \frac{P}{R c}$$

$$T_{out} = \frac{P}{R c} - T_{in}$$

A calorimeter of mass $$m_c$$ and specific heat $$c_c$$ contains a liquid of mass $$m_L$$ and specific heat $$c_L$$. If energy $$Q$$ is added to the system, which expression represents the common temperature change $$\Delta T$$?

$$\Delta T = \frac{Q}{m_c c_c + m_L c_L}$$

$$\Delta T = \frac{Q}{m_c c_c - m_L c_L}$$

$$\Delta T = \frac{Q (m_c c_c)}{m_L c_L}$$

$$\Delta T = Q(m_c c_c + m_L c_L)$$

A solar collector with area $$A$$ absorbs solar radiation of intensity $$I$$ (power per unit area) with efficiency $$e$$. It heats a fluid of mass $$m$$ and specific heat $$c$$. Which expression represents the rate of temperature change $$\frac{dT}{dt}$$?

$$\frac{dT}{dt} = \frac{e I A}{m c}$$

$$\frac{dT}{dt} = \frac{I A}{e m c}$$

$$\frac{dT}{dt} = \frac{e I m}{A c}$$

$$\frac{dT}{dt} = \frac{m c}{e I A}$$

Two spheres, A and B, receive the same amount of heat energy $$Q$$. Sphere A has mass $$m$$ and specific heat $$c$$. Sphere B has mass $$2m$$ and specific heat $$\frac{c}{2}$$. Which expression correctly compares the temperature change of sphere A ($$\Delta T_A$$) to sphere B ($$\Delta T_B$$)?

$$\Delta T_A = \frac{1}{2} \Delta T_B$$

AP Physics 2 Unit 9 Practice Test

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unit 9 unit 10 unit 11 unit 12 unit 13 unit 14 unit 15

Thermodynamics

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The exam experience, sized to one unit — timed like the real thing

20 Multiple Choice Questions

40 min

1 FRQ – FRQ 1 – Mathematical Routines

24 min

1 FRQ – FRQ 2 – Translation Between Representations

24 min

Sections run back-to-back with the same directions, timers, and scoring as the real exam

Total: 1 hr 28 min

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multiple choice questions

free response questions (choose as many as you want)

FRQ 1 – Mathematical Routines · 24 minFRQ 2 – Translation Between Representations · 24 minFRQ 3 – Experimental Design · 24 minFRQ 4 – Qualitative/Quantitative Translation · 24 min

Total: 40 min

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AP Physics 2 Unit 9 practice questions

Try 10 multiple-choice questions from Unit 9 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.

Question 1
A heating element with power output $P$ transfers energy to a liquid of mass $m$ and specific heat $c$ . If the liquid's temperature increases from $T_i$ to $T_f$ with no heat loss, which expression represents the time $t$ required?
$t = \frac{mc(T_f - T_i)}{P}$
$t = \frac{P}{mc(T_f - T_i)}$
$t = \frac{mcP}{(T_f - T_i)}$
$t = mc(T_f - T_i)P$
Show answer
Answer: (A)
Relating energy, power, and temperature change leads to the correct time expression. Since $Q = mc\Delta T$ and $Q = Pt$ , equating them gives $Pt = mc(T_f - T_i)$ , which solves to $t = \frac{mc(T_f - T_i)}{P}$ .
Question 2
A block of mass $M$ and specific heat $C_B$ at temperature $T_H$ is placed into a liquid of mass $m$ and specific heat $C_L$ at temperature $T_C$ . If the system is isolated, which expression represents the final equilibrium temperature $T_f$ ?
$T_f = \frac{M C_B T_H + m C_L T_C}{M C_B + m C_L}$
$T_f = \frac{M C_B T_H - m C_L T_C}{M C_B - m C_L}$
$T_f = \frac{M C_B T_C + m C_L T_H}{M C_B + m C_L}$
$T_f = \frac{M C_B T_H + m C_L T_C}{M C_B - m C_L}$
Show answer
Answer: (A)
Applying conservation of energy allows for the derivation of the equilibrium temperature. The heat lost by the block ( $M C_B (T_H - T_f)$ ) equals the heat gained by the liquid ( $m C_L (T_f - T_C)$ ), which rearranges to this weighted average.
Question 3
A resistor of resistance $R$ carries a current $I$ while immersed in a liquid of mass $m$ . If the liquid's temperature rises by $\Delta T$ in time $t$ , which expression gives the specific heat $c$ of the liquid?
$c = \frac{I^2 R t}{m \Delta T}$
$c = \frac{I R^2 t}{m \Delta T}$
$c = \frac{I^2 R}{m t \Delta T}$
$c = \frac{I R t}{m \Delta T}$
Show answer
Answer: (A)
Equating electrical energy to thermal energy isolates the specific heat. The electrical energy supplied is $E = I^2 R t$ , and the thermal energy absorbed is $Q = mc\Delta T$ . Setting $I^2 R t = mc\Delta T$ yields the correct expression.
Question 4
A lead bullet of mass $m$ traveling at speed $v$ strikes a target and stops completely. If half of the initial kinetic energy converts to internal energy in the bullet, which expression represents the bullet's temperature change $\Delta T$ ? (Let $c$ be the specific heat of lead).
$\Delta T = \frac{v^2}{4c}$
$\Delta T = \frac{v^2}{2c}$
$\Delta T = \frac{v^2}{c}$
$\Delta T = \frac{2v^2}{c}$
Show answer
Answer: (A)
Converting a fraction of kinetic energy to heat yields the temperature change. Initial KE is $\frac{1}{2}mv^2$ . Half of this is $\frac{1}{4}mv^2$ . Equating to $mc\Delta T$ and canceling $m$ gives $\Delta T = \frac{v^2}{4c}$ .
Question 5
A sample of material has density $\rho$ , volume $V$ , and specific heat $c$ . Which expression represents the energy $Q$ required to increase its temperature by $\Delta T$ ?
$Q = \rho V c \Delta T$
$Q = \frac{\rho c \Delta T}{V}$
$Q = \frac{V c \Delta T}{\rho}$
$Q = \rho V c + \Delta T$
Show answer
Answer: (A)
Substituting density and volume for mass provides the correct energy expression. Since $m = \rho V$ , substituting this into the specific heat equation $Q = mc\Delta T$ results in $Q = \rho V c \Delta T$ .
Question 6
Water flows through a heater at a rate of $R$ (kg/s). The heater provides power $P$ . If the water enters at temperature $T_{in}$ and has specific heat $c$ , which expression gives the exit temperature $T_{out}$ ?
$T_{out} = T_{in} + \frac{P}{R c}$
$T_{out} = T_{in} + \frac{R c}{P}$
$T_{out} = T_{in} - \frac{P}{R c}$
$T_{out} = \frac{P}{R c} - T_{in}$
Show answer
Answer: (A)
Relating power to mass flow rate yields the exit temperature. Power $P$ equals the rate of heat transfer $\frac{Q}{t} = \frac{m}{t} c \Delta T = R c (T_{out} - T_{in})$ . Solving for $T_{out}$ gives the correct expression.
Question 7
A calorimeter of mass $m_c$ and specific heat $c_c$ contains a liquid of mass $m_L$ and specific heat $c_L$ . If energy $Q$ is added to the system, which expression represents the common temperature change $\Delta T$ ?
$\Delta T = \frac{Q}{m_c c_c + m_L c_L}$
$\Delta T = \frac{Q}{m_c c_c - m_L c_L}$
$\Delta T = \frac{Q (m_c c_c)}{m_L c_L}$
$\Delta T = Q(m_c c_c + m_L c_L)$
Show answer
Answer: (A)
Summing the heat capacities of the components correctly determines the temperature change. The total energy $Q$ is distributed between the calorimeter and liquid: $Q = (m_c c_c + m_L c_L)\Delta T$ .
Question 8
A waterfall has height $h$ . If all the change in gravitational potential energy of the water goes into increasing its internal energy, which expression gives the temperature increase $\Delta T$ ? (Let $g$ be acceleration due to gravity and $c$ be the specific heat of water).
$\Delta T = \frac{gh}{c}$
$\Delta T = \frac{mgh}{c}$
$\Delta T = \frac{c}{gh}$
$\Delta T = ghc$
Show answer
Answer: (A)
Equating potential energy change to thermal energy yields the temperature rise. $mgh = mc\Delta T$ . The mass $m$ cancels out, leaving $\Delta T = \frac{gh}{c}$ .
Question 9
A solar collector with area $A$ absorbs solar radiation of intensity $I$ (power per unit area) with efficiency $e$ . It heats a fluid of mass $m$ and specific heat $c$ . Which expression represents the rate of temperature change $\frac{dT}{dt}$ ?
$\frac{dT}{dt} = \frac{e I A}{m c}$
$\frac{dT}{dt} = \frac{I A}{e m c}$
$\frac{dT}{dt} = \frac{e I m}{A c}$
$\frac{dT}{dt} = \frac{m c}{e I A}$
Show answer
Answer: (A)
Relating absorbed power to the rate of internal energy change provides the solution. Input power is $P_{in} = eIA$ . Since $P = mc(\frac{dT}{dt})$ , solving for the rate gives $\frac{dT}{dt} = \frac{eIA}{mc}$ .
Question 10
Two spheres, A and B, receive the same amount of heat energy $Q$ . Sphere A has mass $m$ and specific heat $c$ . Sphere B has mass $2m$ and specific heat $\frac{c}{2}$ . Which expression correctly compares the temperature change of sphere A ( $\Delta T_A$ ) to sphere B ( $\Delta T_B$ )?
$\Delta T_A = \Delta T_B$
$\Delta T_A = 2 \Delta T_B$
$\Delta T_A = 4 \Delta T_B$
$\Delta T_A = \frac{1}{2} \Delta T_B$
Show answer
Answer: (A)
Calculating the temperature change for both spheres reveals they are equal. For A: $\Delta T_A = \frac{Q}{mc}$ . For B: $\Delta T_B = \frac{Q}{(2m)(c/2)} = \frac{Q}{mc}$ . Thus, the changes are identical.

What's on the AP Physics 2 Unit 9 practice test

The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:

20 Multiple Choice Questions (40 minutes)
1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

Questions are drawn from 1243 multiple-choice questions and 24 FRQs written for Unit 9, Thermodynamics.

Practice AP Physics 2 Unit 9 FRQs

Answer the unit's free-response questions one at a time and get a score on every part.

FRQ 1 – Mathematical Routines (2 questions)
FRQ 2 – Translation Between Representations (5 questions)
FRQ 3 – Experimental Design (4 questions)
FRQ 4 – Qualitative/Quantitative Translation (13 questions)

AP Physics 2 Unit 9 Practice Test

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