Q: A 0.500 kg aluminum pan is used to heat 0.250 kg of water from 20.0°C to 80.0°C. The specific heat of water is 4186 J/kg°C and that of aluminum is 900 J/kg°C. What is the total heat required?

$$Q = (0.500 \times 900 \times 60) + (0.250 \times 4186 \times 60) = 27,000 + 62,790 = 89,790 J$$

Q: A 1.0 g sample of water is heated from 14.5°C to 15.5°C. The specific heat of water is 4.186 J/g°C. How much heat is required?

$$Q = 1.0 \times 4.186 \times (15.5 - 14.5) = 4.186 J$$

Q: A 70 kg person climbs 1,000 stairs, each 0.18 m high. How much work is done against gravity? (Take $$g = 9.8 m/s$^2)$$

$$W = 70 \times 9.8 \times 0.18 \times 1000 = 123,480 J$$

Q: Which of the following is the correct value for the Boltzmann constant $$k_B$$?

$$k_B = 1.38 \times 10$$^{-23}$$ J/K

Question 1

Which of the following best describes the relationship between the average kinetic energy of a gas molecule and the temperature of the gas?

Accepted Answer

The average kinetic energy is directly proportional to the absolute temperature: $$K_{ave} = \frac{3}{2} k_B T.$$

Question 2

If the root-mean-square speed ($$v_{rms}) of $$the molecules in a sample of nitrogen gas is doubled, by what factor does the temperature of the gas change?

Accepted Answer

It increases by a factor of 4.

Question 3

The mean free path $$\lambda of a $$gas molecule is given by $$\lambda = \frac{k_B T}{2 \pi d^2$ P}. If $$the pressure is doubled while temperature and molecular diameter remain constant, what happens to the mean free path?

Accepted Answer

It is halved.

Question 4

Which of the following statements about the specific heat capacity $$c is $$correct?

Accepted Answer

It is the amount of heat required to raise the temperature of 1 kg of a substance by 1 K.

Question 5

A 0.500 kg aluminum pan is used to heat 0.250 kg of water from 20.0°C to 80.0°C. The specific heat of water is 4186 J/kg°C and that of aluminum is 900 J/kg°C. What is the total heat required?

Accepted Answer

$$Q = (0.500 	imes 900 	imes 60) + (0.250 	imes 4186 	imes 60) = 27,000 + 62,790 = 89,790 J$$

Question 6

Which of the following is a correct statement about the internal energy $$U of a $$system?

Accepted Answer

It is the sum of the kinetic and potential energies of all molecules in the system.

Question 7

If two objects made of the same material but with different masses and temperatures are placed in thermal contact, which of the following best describes the final equilibrium temperature?

Accepted Answer

It will be closer to the temperature of the object with greater mass.

Question 8

Which equation correctly relates the pressure, volume, and temperature of an ideal gas using the number of molecules $$N$$?

Accepted Answer

$$pV = Nk_B T$$

Question 9

A 1.0 g sample of water is heated from 14.5°C to 15.5°C. The specific heat of water is 4.186 J/g°C. How much heat is required?

Accepted Answer

$$Q = 1.0 	imes 4.186 	imes (15.5 - 14.5) = 4.186 J$$

Question 10

Which of the following best describes the difference between temperature and thermal energy?

Accepted Answer

Temperature is a measure of the average kinetic energy; thermal energy is the total kinetic energy of all molecules.

Question 11

If the diameter $$d of $$gas molecules is decreased while keeping temperature and pressure constant, what happens to the mean free path $$\lambda$$?

Accepted Answer

It increases.

Question 12

Which of the following is NOT a possible result of adding heat to a substance?

Accepted Answer

A decrease in temperature.

Question 13

A 70 kg person climbs 1,000 stairs, each 0.18 m high. How much work is done against gravity? (Take $$g = 9.8 m/s$^2)$$

Accepted Answer

$$W = 70 	imes 9.8 	imes 0.18 	imes 1000 = 123,480 J$$

Question 14

Which of the following is the correct value for the Boltzmann constant $$k_B$$?

Accepted Answer

$$k_B = 1.38 	imes 10$$^{-23}$$ J/K

Question 15

Which of the following best describes the process of thermal equilibrium?

Accepted Answer

It is reached when two objects in thermal contact have the same temperature.

Thermodynamics II: Kinetic Theory, Specific Heat, and Heat Transfer

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