Q: A steel bridge expands by $$1.2 cm $$when the temperature increases by $$30^ ext{o}C. If $$the coefficient of linear expansion for steel is $$1.2 \times 10$$^{-5}$$~\text{K}^{-1}$$, what is the original length of the bridge?

$$L_0$$ = \frac{\Delta L}{\alpha \Delta T} = \frac{0.012~\text{m}}{1.2 \times $$10^{-5}$$~\text{K}^{-1} \times 30~\text{K}} = 33.3~\text{m}$$

Q: Which of the following statements about the Kelvin temperature scale is correct?

Absolute zero ($$0~\text{K}) is $$the temperature at which all molecular motion theoretically stops.

Q: A $$0.5~\text{kg}$$ block of copper ($$c_{\text{Cu}} = 385~\text{J/kg}\cdot^\circ\text{C}) is $$heated from $$20~^\circ\text{C} to$$ $$80~^\circ\text{C}. $$How much heat is required?

$$Q = mc\Delta T = 0.5 \times 385 \times (80-20) = 11,550~\text{J}$$

Q: A black body ($$e=1) $$with surface area $$2~\text{m}^2 is at$$ $$T = 400~\text{K} in an $$environment at $$T_{\text{env}} = 300~\text{K}. $$Using the Stefan-Boltzmann law, which expression gives the net power radiated?

$$P = \sigma e A (T^4$ - T_{\text{env}}^4) = \sigma \times 1 \times 2 \times (400^4$ - 300^4$)$$

Question 1

Which of the following best describes the Zeroth Law of Thermodynamics?

Accepted Answer

If two bodies are in thermal equilibrium with a third body, then they are in thermal equilibrium with each other: $$T_A = T_B$$ and $$T_B = T_C \implies T_A = T_C.$$

Question 2

A thermometer is placed in thermal contact with a cup of water. Which statement is correct about the process?

Accepted Answer

The thermometer and water exchange heat until they reach the same temperature, at which point thermal equilibrium is achieved.

Question 3

A steel bridge expands by $$1.2 cm $$when the temperature increases by $$30^	ext{o}C. If $$the coefficient of linear expansion for steel is $$1.2 	imes 10$$^{-5}$$~	ext{K}^{-1}$$, what is the original length of the bridge?

Accepted Answer

$$L_0$$ = \frac{\Delta L}{\alpha \Delta T} = \frac{0.012~	ext{m}}{1.2 	imes $$10^{-5}$$~	ext{K}^{-1} 	imes 30~	ext{K}} = 33.3~	ext{m}$$

Question 4

Which of the following statements about the Kelvin temperature scale is correct?

Accepted Answer

Absolute zero ($$0~	ext{K}) is $$the temperature at which all molecular motion theoretically stops.

Question 5

A $$0.5~	ext{kg}$$ block of copper ($$c_{	ext{Cu}} = 385~	ext{J/kg}\cdot^\circ	ext{C}) is $$heated from $$20~^\circ	ext{C} to$$ $$80~^\circ	ext{C}. $$How much heat is required?

Accepted Answer

$$Q = mc\Delta T = 0.5 	imes 385 	imes (80-20) = 11,550~	ext{J}$$

Question 6

Which mechanism of heat transfer is primarily responsible for the warming of air near a radiator in a room?

Accepted Answer

Convection, because warm air rises and cooler air sinks, creating currents.

Question 7

A metal rod of length $$L$$ and cross-sectional area $$A$$ connects two heat reservoirs at temperatures $$T_1$$ and $$T_2$$ ($$T_1$$ \u003e $$T_2). $$According to the conduction equation, which change will double the rate of heat transfer $$P$$?

Accepted Answer

Doubling the cross-sectional area $$A$$ while keeping all other variables constant.

Question 8

A black body ($$e=1) $$with surface area $$2~	ext{m}^2 is at$$ $$T = 400~	ext{K} in an $$environment at $$T_{	ext{env}} = 300~	ext{K}. $$Using the Stefan-Boltzmann law, which expression gives the net power radiated?

Accepted Answer

$$P = \sigma e A (T^4$ - T_{	ext{env}}^4) = \sigma 	imes 1 	imes 2 	imes (400^4$ - 300^4$)$$

Question 9

Which of the following best explains why metals feel colder than wood at the same temperature?

Accepted Answer

Metals have a higher thermal conductivity $$k$$, so they conduct heat away from your hand more rapidly.

Question 10

A $$100~	ext{g}$$ sample of water at $$20~^\circ	ext{C}$$ absorbs $$4186~	ext{J} of $$heat. What is its final temperature? ($$c_{	ext{water}} = 4186~	ext{J/kg}\cdot^\circ	ext{C})$$

Accepted Answer

$$Q = mc\Delta T \implies \Delta T = \frac{Q}{mc} = \frac{4186}{0.1 	imes 4186} = 10~^\circ	ext{C}$$, so final temperature is $$30~^\circ	ext{C}.$$

Question 11

Which of the following is NOT a correct statement about heat capacity and specific heat?

Accepted Answer

Specific heat $$c$$ depends on the mass of the object.

Question 12

A $$0.2~	ext{kg}$$ aluminum pan ($$c_{	ext{Al}} = 900~	ext{J/kg}\cdot^\circ	ext{C}) at$$ $$25~^\circ	ext{C} is $$placed on a stove and absorbs $$18,000~	ext{J} of $$heat. What is its final temperature?

Accepted Answer

$$\Delta T = \frac{Q}{mc} = \frac{18,000}{0.2 	imes 900} = 100~^\circ	ext{C}$$; final temperature is $$125~^\circ	ext{C}.$$

Question 13

Which of the following scenarios best illustrates thermal equilibrium?

Accepted Answer

A hot metal spoon placed in a cup of cold water eventually reaches the same temperature as the water.

Question 14

Which of the following is a correct conversion between Celsius and Kelvin?

Accepted Answer

$$T(	ext{K}) = t(^\circ	ext{C}) + 273.15$$

Question 15

A window pane has an area of $$1.5~	ext{m}^2$$, thickness $$0.005~	ext{m}$$, and thermal conductivity $$k = 0.8~	ext{W/m}\cdot	ext{K}. If $$the temperature difference across the pane is $$20~	ext{K}$$, what is the rate of heat transfer through the glass?

Accepted Answer

$$P = \frac{kA\Delta T}{L} = \frac{0.8 	imes 1.5 	imes 20}{0.005} = 4800~	ext{W}$$

Question 16

Which of the following is the best example of heat transfer by radiation?

Accepted Answer

The Sun warming your skin on a clear day.

Question 17

A $$0.3~	ext{kg}$$ block of ice at $$0~^\circ	ext{C} is $$placed in $$0.5~	ext{kg} of $$water at $$30~^\circ	ext{C}. $$Assuming no heat loss to the environment and $$c_{	ext{water}} = 4186~	ext{J/kg}\cdot^\circ	ext{C}$$, how much heat is required to melt the ice? (Latent heat of fusion for ice $$L_f = 334,000~	ext{J/kg})$$

Accepted Answer

$$Q = m L_f = 0.3 	imes 334,000 = 100,200~	ext{J}$$

Question 18

Which of the following statements about the microscopic view of thermal energy is correct?

Accepted Answer

Even when a body is at rest, its molecules possess kinetic energy due to random vibrations.

Lecture 16

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