Q: Two 1-kg objects are put in thermal contact and insulated. Their initial temperatures are $$T_1 = 100$$^\circ$$C and T_2$ = 0^\circC$$, with specific heats $$c_1 = 300$ J/kg·K and c_2$ = 900 J/kg$$·K. What is the final equilibrium temperature $$T_f$$?

$$T_f = 25^\circC$$ + \frac{900}{1200} \times 100^\circ$$C = 75^\circC$$

Q: A 2-kg block of copper ($$c = 390 J/kg$$·K) is heated from $$20^\circC to$$ $$50^\circC. $$How much heat is required?

$$Q = 2 \times 390 \times (50 - 20) = 23,400 J$$

Question 1

Which equation correctly describes the total change in length $$\Delta L_{tot} of a $$rod subjected to both thermal expansion and mechanical stress?

Accepted Answer

$$\Delta L_{tot} = \alpha L_0$ \Delta T + \frac{L_0$ F}{A Y}$$

Question 2

Four rods are connected end-to-end in a rigid frame and heated. If the rods cannot separate, which constraint must be satisfied by their length changes $$\Delta L_1$, \Delta L_2$, \Delta L_3$, \Delta L_4$?

Accepted Answer

$$\Delta L_1$ + \Delta L_2$ + \Delta L_3$ + \Delta L_4$ = 0$$

Question 3

If three compressive forces $$F_2$$, $$F_3$$, $$F_4$$ act on three rods in a rigid system, what is the correct relationship between them?

Accepted Answer

$$F_2$$ + $$F_3$$ + $$F_4 = 0$

Question 4

Two objects of equal mass, one at $$100^\circC $$and one at $$0^\circC$$, are placed in thermal contact and insulated from the environment. What is the final equilibrium temperature?

Accepted Answer

It will be $$50^\circC $$only if their specific heats are equal.

Question 5

Which equation gives the heat $$Q$$ required to raise the temperature of a mass $$m of a $$substance with specific heat $$c by$$ $$\Delta T$$?

Accepted Answer

$$Q = m c \Delta T$$

Question 6

If you plot temperature versus energy added for two liquids of equal mass, but one has a larger specific heat, how does the slope of the temperature vs. energy graph compare?

Accepted Answer

The slope is smaller for the liquid with larger specific heat.

Question 7

What are the units of specific heat $$c$$?

Accepted Answer

$$\mathrm{J/(kg \cdot K)}$$

Question 8

Which of the following best explains why some materials have larger heat capacities than others?

Accepted Answer

Some energy goes into molecular rotations and vibrations, not just translational motion.

Question 9

Two 1-kg objects are put in thermal contact and insulated. Their initial temperatures are $$T_1 = 100$$^\circ$$C and T_2$ = 0^\circC$$, with specific heats $$c_1 = 300$ J/kg·K and c_2$ = 900 J/kg$$·K. What is the final equilibrium temperature $$T_f$$?

Accepted Answer

$$T_f = 25^\circC$$ + \frac{900}{1200} 	imes 100^\circ$$C = 75^\circC$$

Question 10

Which equation gives the heat $$Q$$ required to raise the temperature of $$n$$ moles of a substance with molar heat capacity $$C by$$ $$\Delta T$$?

Accepted Answer

$$Q = n C \Delta T$$

Question 11

A 2-kg block of copper ($$c = 390 J/kg$$·K) is heated from $$20^\circC to$$ $$50^\circC. $$How much heat is required?

Accepted Answer

$$Q = 2 	imes 390 	imes (50 - 20) = 23,400 J$$

Question 12

Which of the following statements about heat and temperature is correct?

Accepted Answer

Heat is energy transferred due to temperature differences.

Question 13

A 1-kg sample of ethanol ($$c = 2428 J/kg$$·K) and a 1-kg sample of aluminum ($$c = 910 J/kg$$·K) are both heated by 1000 J. Which will experience the greater temperature change?

Accepted Answer

Aluminum, because it has a lower specific heat.

Question 14

Which of the following best describes the physical meaning of specific heat?

Accepted Answer

The energy required to raise 1 kg of a substance by 1 K.

Question 15

A 0.5-kg block of copper ($$c = 390 J/kg$$·K) at $$80^\circC is $$placed in 1 kg of water ($$c = 4186 J/kg$$·K) at $$20^\circC. $$What is the best estimate for the final equilibrium temperature?

Accepted Answer

Closer to $$20^\circC $$than $$80^\circC$$

Question 16

Why does water have a much higher specific heat than most metals?

Accepted Answer

Water molecules have more degrees of freedom (rotational, vibrational) to absorb energy.

Question 17

If you add 1000 J of heat to 1 mole of copper ($$C = 24.8 J/$$mol·K), what is the temperature change?

Accepted Answer

$$\Delta T = \frac{1000}{24.8} = 40.3 K$$

Heat, Specific Heat, and Thermal Equilibrium: Physics with Calculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards