---
title: "AP Physics 2 Unit 9 Practice Test"
description: "A timed AP Physics 2 Unit 9 (Thermodynamics) practice test in the AP format, drawn from 1,243 multiple-choice questions and 24 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-2-revised/unit-test/9"
type: "unit-test"
subject: "AP Physics 2"
unit: "Unit 9"
---

# AP Physics 2 Unit 9 Practice Test

## Overview

A timed AP Physics 2 Unit 9 (Thermodynamics) practice test in the AP format, drawn from 1,243 multiple-choice questions and 24 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

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

## Unit FRQs by Type

- [FRQ 1 – Mathematical Routines](/ap-physics-2-revised/frqs/mathematical-routines?unit=9): 2 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-2-revised/frqs/translation-between-representations?unit=9): 5 questions
- [FRQ 3 – Experimental Design](/ap-physics-2-revised/frqs/experimental-design?unit=9): 4 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-2-revised/frqs/qualitative-quantitative-translation?unit=9): 13 questions

## Practice Questions

### 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?

- (A) $$t = \frac{mc(T_f - T_i)}{P}$$
- (B) $$t = \frac{P}{mc(T_f - T_i)}$$
- (C) $$t = \frac{mcP}{(T_f - T_i)}$$
- (D) $$t = mc(T_f - T_i)P$$

**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 $$T_f$$?

- (A) $$T_f = \frac{M C_B T_H + m C_L T_C}{M C_B + m C_L}$$
- (B) $$T_f = \frac{M C_B T_H - m C_L T_C}{M C_B - m C_L}$$
- (C) $$T_f = \frac{M C_B T_C + m C_L T_H}{M C_B + m C_L}$$
- (D) $$T_f = \frac{M C_B T_H + m C_L T_C}{M C_B - m C_L}$$

**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?

- (A) $$c = \frac{I^2 R t}{m \Delta T}$$
- (B) $$c = \frac{I R^2 t}{m \Delta T}$$
- (C) $$c = \frac{I^2 R}{m t \Delta T}$$
- (D) $$c = \frac{I R t}{m \Delta T}$$

**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).

- (A) $$\Delta T = \frac{v^2}{4c}$$
- (B) $$\Delta T = \frac{v^2}{2c}$$
- (C) $$\Delta T = \frac{v^2}{c}$$
- (D) $$\Delta T = \frac{2v^2}{c}$$

**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 $$\Delta T$$?

- (A) $$Q = \rho V c \Delta T$$
- (B) $$Q = \frac{\rho c \Delta T}{V}$$
- (C) $$Q = \frac{V c \Delta T}{\rho}$$
- (D) $$Q = \rho V c + \Delta T$$

**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 $$T_{out}$$?

- (A) $$T_{out} = T_{in} + \frac{P}{R c}$$
- (B) $$T_{out} = T_{in} + \frac{R c}{P}$$
- (C) $$T_{out} = T_{in} - \frac{P}{R c}$$
- (D) $$T_{out} = \frac{P}{R c} - T_{in}$$

**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 $$\Delta T$$?

- (A) $$\Delta T = \frac{Q}{m_c c_c + m_L c_L}$$
- (B) $$\Delta T = \frac{Q}{m_c c_c - m_L c_L}$$
- (C) $$\Delta T = \frac{Q (m_c c_c)}{m_L c_L}$$
- (D) $$\Delta T = Q(m_c c_c + m_L c_L)$$

**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).

- (A) $$\Delta T = \frac{gh}{c}$$
- (B) $$\Delta T = \frac{mgh}{c}$$
- (C) $$\Delta T = \frac{c}{gh}$$
- (D) $$\Delta T = ghc$$

**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 $$\frac{dT}{dt}$$?

- (A) $$\frac{dT}{dt} = \frac{e I A}{m c}$$
- (B) $$\frac{dT}{dt} = \frac{I A}{e m c}$$
- (C) $$\frac{dT}{dt} = \frac{e I m}{A c}$$
- (D) $$\frac{dT}{dt} = \frac{m c}{e I A}$$

**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 ($$\Delta T_B$$)?

- (A) $$\Delta T_A = \Delta T_B$$
- (B) $$\Delta T_A = 2 \Delta T_B$$
- (C) $$\Delta T_A = 4 \Delta T_B$$
- (D) $$\Delta T_A = \frac{1}{2} \Delta T_B$$

**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.

## Review the Unit

- [9.1 Kinetic Theory of Temperature and Pressure](/ap-physics-2-revised/unit-9/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3)
- [9.2 The Ideal Gas Law](/ap-physics-2-revised/unit-9/2-the-ideal-gas-law/study-guide/Nw3xH5qnLmpzH8F0)
- [9.3 Thermal Energy Transfer and Equilibrium](/ap-physics-2-revised/unit-9/3-thermal-energy-transfer-and-equilibrium/study-guide/B2UC1jOK2bqVTMMH)
- [9.4 The First Law of Thermodynamics](/ap-physics-2-revised/unit-9/4-the-first-law-of-thermodynamics/study-guide/MDiIPIbllDYW1klR)
- [9.5 Specific Heat and Thermal Conductivity](/ap-physics-2-revised/unit-9/5-specific-heat-and-thermal-conductivity/study-guide/VTemzlLtvNgPkUnm)
- [9.6 Entropy and the Second Law of Thermodynamics](/ap-physics-2-revised/unit-9/6-entropy-and-the-second-law-of-thermodynamics/study-guide/sddxT6j4BT0uuqO5)

## Other Unit Tests

- [Unit 10: Electric Force, Field, and Potential](/ap-physics-2-revised/unit-test/10)
- [Unit 11: Electric Circuits](/ap-physics-2-revised/unit-test/11)
- [Unit 12: Magnetism and Electromagnetism](/ap-physics-2-revised/unit-test/12)
- [Unit 13: Geometric Optics](/ap-physics-2-revised/unit-test/13)
- [Unit 14: Waves, Sound, and Physical Optics](/ap-physics-2-revised/unit-test/14)
- [Unit 15: Modern Physics](/ap-physics-2-revised/unit-test/15)

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