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?

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

Q: If 1000 J of heat is added to 0.5 kg of water ($$c = 4186 J/kg$$·K), what is the temperature change?

$$\Delta T = \frac{1000}{0.5 \times 4186} \approx 0.48 K$$

Q: A scientist wants to heat 1 mole of ethanol ($$C = 111.9 J/$$mol·K) by $$10 K. $$How much energy is required?

$$Q = 1 \times 111.9 \times 10 = 1119 J$$

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 changes in length $$\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, which relation must be satisfied for equilibrium?

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 (y-axis) versus total energy transferred (x-axis) for a liquid, what happens to the slope if you repeat the experiment with a liquid of the same mass but larger specific heat?

Accepted Answer

The slope becomes smaller.

Question 7

What is the physical meaning of specific heat $$c$$?

Accepted Answer

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

Question 8

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 9

Why do more complex molecules generally have higher specific heats?

Accepted Answer

Because energy added can go into rotational and vibrational modes, not just translational motion.

Question 10

Two 1-kg objects are put in thermal contact and insulated from the environment. 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 = 75^\circC$

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 best describes the process of reaching thermal equilibrium between two objects in thermal contact?

Accepted Answer

Heat flows from the hotter object to the colder one until both reach the same temperature.

Question 13

If 1000 J of heat is added to 0.5 kg of water ($$c = 4186 J/kg$$·K), what is the temperature change?

Accepted Answer

$$\Delta T = \frac{1000}{0.5 	imes 4186} \approx 0.48 K$$

Question 14

Which material would require the most energy to raise the temperature of 1 kg by 1 K, based on the provided table?

Accepted Answer

Beryllium ($$c = 1970 J/kg$$·K)

Question 15

A scientist wants to heat 1 mole of ethanol ($$C = 111.9 J/$$mol·K) by $$10 K. $$How much energy is required?

Accepted Answer

$$Q = 1 	imes 111.9 	imes 10 = 1119 J$$

Question 16

Why does the temperature of a substance not always increase linearly with the amount of heat added?

Accepted Answer

Some energy may go into changing the phase or into rotational/vibrational modes.

Question 17

Which of the following is a correct unit for molar heat capacity $$C$$?

Accepted Answer

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

Question 18

A 1-kg block of aluminum ($$c = 910 J/kg$$·K) and a 1-kg block of copper ($$c = 390 J/kg$$·K) are both heated with 1000 J of energy. Which block experiences the greater temperature change?

Accepted Answer

Copper, because it has a lower specific heat.

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

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