Q: A constant-volume gas thermometer records a pressure of $$240\ \mathrm{mmHg} at $$the ice point and $$300\ \mathrm{mmHg} at $$the steam point. What is the temperature when the pressure is $$280\ \mathrm{mmHg}$$?

$$T = \frac{280-240}{300-240} \times 100 + 0 = 66.7^\circ \mathrm{C}$$

Q: A steel rod of length $$30.00\ \mathrm{m} at$$ $$0.0^\circ \mathrm{C} is $$heated to $$40.0^\circ \mathrm{C}. If $$the coefficient of linear expansion is $$11 \times 10$$^{-6}$$\ ^\circ \mathrm{C}^{-1}$$, what is its new length?

$$L_f = 30.00 + 30.00 \times 11 \times 10$$^{-6}$$ \times 40.0 = 30.013\ \mathrm{m}$$

Q: A $$0.05\ \mathrm{kg}$$ metal ingot at $$200.0^\circ \mathrm{C} is $$dropped into $$0.4\ \mathrm{kg} of $$water at $$20.0^\circ \mathrm{C}. $$The final temperature is $$22.4^\circ \mathrm{C}. If $$the specific heat of water is $$4186\ \mathrm{J/kg\cdot K}$$, what is the specific heat of the metal?

$$c_m = \frac{0.4 \times 4186 \times (22.4-20.0)}{0.05 \times (200.0-22.4)} = 4.53 \times 10^2$\ \mathrm{J/kg\cdot K}$$

Q: A gas is compressed from $$9.00\ \mathrm{m}^3 to$$ $$2.00\ \mathrm{m}^3 at a $$constant pressure of $$0.8\ \mathrm{atm}. If$$ $$400\ \mathrm{J} of $$energy leaves the gas by heat, what is the change in internal energy? ($$1\ \mathrm{atm} = 1.01 \times 10^5$\ \mathrm{Pa})$$

$$\Delta E_{int} = -400 - [0.8 \times 1.01 \times 10^5$ \times (2.00-9.00)] = 5.65 \times 10^5$\ \mathrm{J}$$

Question 1

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

Accepted Answer

If two objects are in thermal equilibrium with a third object, they are in thermal equilibrium with each other.

Question 2

A constant-volume gas thermometer records a pressure of $$240\ \mathrm{mmHg} at $$the ice point and $$300\ \mathrm{mmHg} at $$the steam point. What is the temperature when the pressure is $$280\ \mathrm{mmHg}$$?

Accepted Answer

$$T = \frac{280-240}{300-240} 	imes 100 + 0 = 66.7^\circ \mathrm{C}$$

Question 3

Which of the following is the correct relationship between Celsius and Kelvin temperature scales?

Accepted Answer

$$T_K = T_C + 273.15$$

Question 4

A steel rod of length $$30.00\ \mathrm{m} at$$ $$0.0^\circ \mathrm{C} is $$heated to $$40.0^\circ \mathrm{C}. If $$the coefficient of linear expansion is $$11 	imes 10$$^{-6}$$\ ^\circ \mathrm{C}^{-1}$$, what is its new length?

Accepted Answer

$$L_f = 30.00 + 30.00 	imes 11 	imes 10$$^{-6}$$ 	imes 40.0 = 30.013\ \mathrm{m}$$

Question 5

Which of the following equations correctly relates the change in volume of a solid to its coefficient of linear expansion $$\alpha$$?

Accepted Answer

$$\Delta V = 3\alpha V_i \Delta T$$

Question 6

A $$0.05\ \mathrm{kg}$$ metal ingot at $$200.0^\circ \mathrm{C} is $$dropped into $$0.4\ \mathrm{kg} of $$water at $$20.0^\circ \mathrm{C}. $$The final temperature is $$22.4^\circ \mathrm{C}. If $$the specific heat of water is $$4186\ \mathrm{J/kg\cdot K}$$, what is the specific heat of the metal?

Accepted Answer

$$c_m = \frac{0.4 	imes 4186 	imes (22.4-20.0)}{0.05 	imes (200.0-22.4)} = 4.53 	imes 10^2$\ \mathrm{J/kg\cdot K}$$

Question 7

Which of the following best describes the first law of thermodynamics for a closed system?

Accepted Answer

$$\Delta E_{int} = Q - W$$

Question 8

A gas is compressed from $$9.00\ \mathrm{m}^3 to$$ $$2.00\ \mathrm{m}^3 at a $$constant pressure of $$0.8\ \mathrm{atm}. If$$ $$400\ \mathrm{J} of $$energy leaves the gas by heat, what is the change in internal energy? ($$1\ \mathrm{atm} = 1.01 	imes 10^5$\ \mathrm{Pa})$$

Accepted Answer

$$\Delta E_{int} = -400 - [0.8 	imes 1.01 	imes 10^5$ 	imes (2.00-9.00)] = 5.65 	imes 10^5$\ \mathrm{J}$$

Question 9

For a monoatomic ideal gas, what is the average translational kinetic energy per molecule at temperature $$T$$?

Accepted Answer

$$\frac{3}{2} k_B T$$

Question 10

Which of the following is NOT an assumption of the kinetic theory of gases?

Accepted Answer

The forces between molecules are significant except during collisions.

Question 11

A Carnot engine operates between $$T_h = 850\ \mathrm{K}$$ and $$T_c = 300\ \mathrm{K}. $$What is its maximum possible efficiency?

Accepted Answer

$$e = 1 - \frac{T_c}{T_h} = 1 - \frac{300}{850} = 0.647$$

Question 12

Which of the following processes is characterized by no heat exchange with the surroundings?

Accepted Answer

Adiabatic process

Question 13

A refrigerator extracts $$Qc$$ from a cold reservoir and expels $$Qh to a $$hot reservoir. What is the coefficient of performance (COP) for cooling mode?

Accepted Answer

$$COP = \frac{|Q_c|}{|Q_h| - |Q_c|}$$

Question 14

Which of the following best describes the third law of thermodynamics?

Accepted Answer

The entropy of a perfect crystal at absolute zero is zero.

Question 15

A wall is made of two materials in series, each with thickness $$L_1$$ and $$L_2$$ and thermal conductivities $$k_1$$ and $$k_2. $$What is the total rate of heat transfer through the wall?

Accepted Answer

$$P = \frac{A (T_h - T_c)}{\frac{L_1$}{k_1$} + \frac{L_2$}{k_2$}}$$

Question 16

According to the molecular interpretation of temperature, which of the following is true?

Accepted Answer

Temperature is proportional to the average translational kinetic energy of molecules.

Question 17

Which of the following statements about heat engines is correct?

Accepted Answer

No real heat engine operating between two reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.

Heat and Thermodynamics: Structured Study Notes for PHY 103

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