Q: A 300 mL cup of coffee at $$90^\circC is $$cooled to $$60^\circC by $$adding ice at $$-20^\circC. If $$the specific heat of coffee is $$4.18 \text{ kJ/kg K}$$, the latent heat of fusion of ice is $$334 \text{ kJ/kg}$$, and the specific heat of ice is $$2.09 \text{ kJ/kg K}$$, which equation would you use to solve for the mass of ice required?

$$Q_{\text{coffee}} + Q_{\text{ice warming}} + Q_{\text{ice melting}} + Q_{\text{water warming}} = 0$$

Question 1

Which of the following best describes Avogadro's Law?

Accepted Answer

At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas: $$V \propto n$$

Question 2

A sample of an ideal gas undergoes an isothermal expansion from volume $$V_1 to$$ $$V_2 at $$temperature $$T. $$What is the work done by the gas during this process?

Accepted Answer

$$W = nRT \ln \left( \frac{V_2$}{V_1$} \right)$$

Question 3

Which equation correctly relates the change in internal energy $$\Delta U of an $$ideal monatomic gas to its temperature change $$\Delta T$$?

Accepted Answer

$$\Delta U = \frac{3}{2} nR \Delta T$$

Question 4

A 300 mL cup of coffee at $$90^\circC is $$cooled to $$60^\circC by $$adding ice at $$-20^\circC. If $$the specific heat of coffee is $$4.18 	ext{ kJ/kg K}$$, the latent heat of fusion of ice is $$334 	ext{ kJ/kg}$$, and the specific heat of ice is $$2.09 	ext{ kJ/kg K}$$, which equation would you use to solve for the mass of ice required?

Accepted Answer

$$Q_{	ext{coffee}} + Q_{	ext{ice warming}} + Q_{	ext{ice melting}} + Q_{	ext{water warming}} = 0$$

Question 5

Which statement about the relationship between temperature and average kinetic energy of a gas is correct?

Accepted Answer

The average kinetic energy of a molecule in an ideal gas is proportional to the absolute temperature: $$\langle E_k \rangle = \frac{3}{2} k_B T$$

Question 6

For a process in which an ideal gas is compressed at constant pressure, which formula gives the work done on the gas?

Accepted Answer

$$W = -P \Delta V$$

Question 7

Which of the following is the correct definition of heat capacity at constant volume ($$C_v) $$for an ideal gas?

Accepted Answer

$$C_v = \left( \frac{\partial U}{\partial T} \right)_V$$

Question 8

A gas undergoes a cyclic process shown on a PV diagram. Which statement is true about the net work done by the gas over one cycle?

Accepted Answer

The net work done by the gas is equal to the area enclosed by the cycle on the PV diagram.

Question 9

Which process is characterized by no heat exchange with the surroundings ($$Q=0$$)?

Accepted Answer

Adiabatic process

Question 10

The first law of thermodynamics can be written as:

Accepted Answer

$$\Delta U = Q - W$$

Question 11

Which of the following best describes the difference between heat and temperature?

Accepted Answer

Heat is energy transferred due to a temperature difference; temperature is a measure of the average kinetic energy of particles.

Question 12

Which equation is used to calculate the degrees of freedom for a molecule and relate it to the molar heat capacities $$C_v$$ and $$C_p$$?

Accepted Answer

$$C_v = \frac{f}{2} R$$, where $$f is $$the degrees of freedom

Question 13

Which of the following is NOT a correct statement about the ideal gas law?

Accepted Answer

It applies to gases at very high pressures and very low temperatures.

Question 14

Which process on a PV diagram is represented by a horizontal line?

Accepted Answer

Isobaric process

Question 15

A gas is heated at constant volume. What is the relationship between the heat added $$Q$$ and the change in internal energy $$\Delta U$$?

Accepted Answer

$$Q = \Delta U$$

Question 16

Which of the following is the correct expression for the root mean square (RMS) speed of molecules in an ideal gas?

Accepted Answer

$$v_{	ext{rms}} = \sqrt{\frac{3k_B T}{m}}$$

Question 17

Which of the following statements about conduction, convection, and radiation is correct?

Accepted Answer

Conduction requires direct contact, convection involves fluid motion, and radiation can occur through a vacuum.

Question 18

If the pressure of an ideal gas is doubled while keeping the temperature constant, what happens to the volume?

Accepted Answer

The volume is halved.

Question 19

Which of the following is the correct conversion from joules to calories?

Accepted Answer

$$1 	ext{ cal} = 4.184 	ext{ J}$$

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