Q: What is the pressure of $$2\ \mathrm{mol} of an $$ideal gas in a volume of $$5\ \mathrm{m}^3 at a $$temperature of $$800\ \mathrm{K}$$? Use $$R = 10\ \mathrm{J/(mol\cdot K)}.$$

$$P = \frac{2 \times 10 \times 800}{5} = 3200\ \mathrm{Pa}$$

Q: A bicycle tire is inflated to a gauge pressure of $$11\ \mathrm{atm} at$$ $$300\ \mathrm{K}. $$The temperature drops to $$250\ \mathrm{K}$$ while the volume remains constant. What is the new gauge pressure? (Atmospheric pressure $$p_0 = 1$$\ \mathrm{atm}$$)

$$P_{new} = (11 + 1) \times \frac{250}{300} - 1 = 9\ \mathrm{atm}$$

Q: What is the change in internal energy $$\Delta E_{th} of$$ $$n = 5\ \mathrm{mol} of a $$monatomic ideal gas when its temperature decreases by $$12\ \mathrm{K}$$? Use $$R = 10\ \mathrm{J/(mol\cdot K)}.$$

$$\Delta E_{th} = n \frac{3}{2} R \Delta T = 5 \times \frac{3}{2} \times 10 \times (-12) = -900\ \mathrm{J}$$

Question 1

A refrigerator operates between a cold reservoir at $$T_C = 273\ \mathrm{K}$$ and a hot reservoir at $$T_H = 400\ \mathrm{K}. $$What is the maximum theoretical coefficient of performance (COP) for this refrigerator?

Accepted Answer

$$\frac{T_C}{T_H - T_C} = \frac{273}{400 - 273} = 2.15$$

Question 2

What is the pressure of $$2\ \mathrm{mol} of an $$ideal gas in a volume of $$5\ \mathrm{m}^3 at a $$temperature of $$800\ \mathrm{K}$$? Use $$R = 10\ \mathrm{J/(mol\cdot K)}.$$

Accepted Answer

$$P = \frac{2 	imes 10 	imes 800}{5} = 3200\ \mathrm{Pa}$$

Question 3

Two identical blocks, A and B, have initial thermal energies $$E_{Ai} = 32\ \mathrm{J}$$ and $$E_{Bi} = 54\ \mathrm{J}$$, respectively. They are thermally connected in an isolated chamber. What is the final energy of block A, $$E_{Af}$$, and the amount of heat exchanged, $$Q$$?

Accepted Answer

$$E_{Af} = 43\ \mathrm{J},\ Q = 11\ \mathrm{J}$$

Question 4

A bicycle tire is inflated to a gauge pressure of $$11\ \mathrm{atm} at$$ $$300\ \mathrm{K}. $$The temperature drops to $$250\ \mathrm{K}$$ while the volume remains constant. What is the new gauge pressure? (Atmospheric pressure $$p_0 = 1$$\ \mathrm{atm}$$)

Accepted Answer

$$P_{new} = (11 + 1) 	imes \frac{250}{300} - 1 = 9\ \mathrm{atm}$$

Question 5

What is the change in internal energy $$\Delta E_{th} of$$ $$n = 5\ \mathrm{mol} of a $$monatomic ideal gas when its temperature decreases by $$12\ \mathrm{K}$$? Use $$R = 10\ \mathrm{J/(mol\cdot K)}.$$

Accepted Answer

$$\Delta E_{th} = n \frac{3}{2} R \Delta T = 5 	imes \frac{3}{2} 	imes 10 	imes (-12) = -900\ \mathrm{J}$$

Question 6

Which of the following is a non-zero quantity for an isothermal process?

Accepted Answer

$$Q$$ for an isothermal process

Question 7

Refer to the second image (triangle pV diagram). Which process has a heat $$Q = 15\ \mathrm{L\cdot atm}$$ for a monatomic gas?

Accepted Answer

None of the processes

Question 8

A sample of $$n = 2\ \mathrm{mol} of $$monatomic ideal gas expands adiabatically from $$V_i = 10\ \mathrm{L} to$$ $$V_f = 20\ \mathrm{L} at an $$initial pressure of $$5\ \mathrm{atm}. $$What is the final pressure?

Accepted Answer

$$P_f = 5 \left(\frac{10}{20}\$$right)^{5/3}$$ = 1.57\ \mathrm{atm}$$

Question 9

For the third image (diagonal line process on a pV diagram), what is the heat $$Q$$ for the process if the gas is monatomic?

Accepted Answer

$$Q = -35\ \mathrm{J}$$

Question 10

An ideal gas increases its temperature by $$36\ ^\circ\mathrm{F}. $$What is this temperature change in Celsius?

Accepted Answer

$$\Delta T = 20\ ^\circ\mathrm{C}$$

Question 11

Refer to the fourth image (two chambers A and B). Chamber A has $$V_A = 4\ \mathrm{m}^3$$, $$n_A = 5\ \mathrm{mol}$$; chamber B has $$V_B = 6\ \mathrm{m}^3$$, $$n_B = 3\ \mathrm{mol}. $$Both are at the same temperature. When the valve is opened, what happens?

Accepted Answer

Gas flows from A to B

Question 12

For the fifth image (Stirling engine pV diagram), what is the fuel heat per cycle $$Q_H$$ for a monatomic gas?

Accepted Answer

$$Q_H = nRT_i (1 + \ln 2)$$

Question 13

A heat engine has a thermal efficiency $$e = \frac{1}{3}. If $$the waste heat per cycle is $$Q_C = -20\ \mathrm{J}$$, what is the work done by the engine per cycle $$W_{eng}$$?

Accepted Answer

$$W_{eng} = 10\ \mathrm{J}$$

Question 14

The closed loop process on the sixth image (rectangular pV diagram) best represents what type of device?

Accepted Answer

Heat engine

Question 15

Suppose the isochoric processes in the Stirling engine (seventh image) are replaced with adiabatic processes, forming a Carnot engine. What is the Carnot efficiency?

Accepted Answer

$$\eta = 1 - \frac{T_C}{T_H} = 1 - \frac{T_i}{3T_i} = \frac{2}{3}$$

Physics with Calculus: Thermodynamics and Ideal Gas Law Study Guide

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