Q: During a quasi-static adiabatic expansion of an ideal gas, which of the following equations must be satisfied?

$$pV^\gamma = \text{constant}$$

Q: A diatomic ideal gas ($$\gamma = 1.4) is $$compressed adiabatically from $$240\ \text{cm}^3 to$$ $$40\ \text{cm}^3. If $$the initial pressure is $$1.00 \times 10^5$\ \text{N/m}^2$$, what is the final pressure?

$$1.23 \times 10^6$\ \text{N/m}^2$$

Q: Which of the following equations represents the adiabatic condition in terms of temperature and volume for an ideal gas?

$$TV^{\gamma-1}$$ = \text{constant}$$

Question 1

Which of the following best describes an adiabatic process for an ideal gas?

Accepted Answer

A process in which no heat is exchanged with the surroundings and all energy transfer is in the form of work.

Question 2

During a quasi-static adiabatic expansion of an ideal gas, which of the following equations must be satisfied?

Accepted Answer

$$pV^\gamma = 	ext{constant}$$

Question 3

In the pV diagram shown, why is the adiabatic curve steeper than the isothermal curve for an ideal gas?

Accepted Answer

Because $$\gamma \u003e 1$$ for an adiabatic process, causing pressure to drop more rapidly with increasing volume.

Question 4

A gas in a thermally insulated cylinder is compressed rapidly. Which of the following statements is true?

Accepted Answer

The temperature of the gas increases because work is done on it.

Question 5

For a reversible adiabatic process of an ideal gas, which of the following relationships holds between the initial and final states?

Accepted Answer

$$p_1V_1^\gamma = p_2V_2^\gamma$$

Question 6

In a free adiabatic expansion of an ideal gas into a vacuum, what happens to the temperature of the gas?

Accepted Answer

It remains constant.

Question 7

Which of the following is the correct expression for the work done by an ideal gas during a quasi-static adiabatic process from $$V_1 to$$ $$V_2$$?

Accepted Answer

$$W = \frac{p_2V_2 - p_1V_1}{1-\gamma}$$

Question 8

A diatomic ideal gas ($$\gamma = 1.4) is $$compressed adiabatically from $$240\ 	ext{cm}^3 to$$ $$40\ 	ext{cm}^3. If $$the initial pressure is $$1.00 	imes 10^5$\ 	ext{N/m}^2$$, what is the final pressure?

Accepted Answer

$$1.23 	imes 10^6$\ 	ext{N/m}^2$$

Question 9

Which of the following best explains why high-octane gasoline is used to prevent engine knocking in car engines?

Accepted Answer

High-octane gasoline has a higher ignition temperature, reducing the chance of spontaneous explosion during adiabatic compression.

Question 10

During a quasi-static adiabatic expansion, which of the following is true about the heat $$Q$$ exchanged by the system?

Accepted Answer

$$Q = 0$$

Question 11

If an ideal gas undergoes a quasi-static adiabatic expansion and its volume doubles, what happens to its temperature?

Accepted Answer

It decreases.

Question 12

Which of the following is the correct relationship for $$\gamma in $$terms of molar heat capacities?

Accepted Answer

$$\gamma = \frac{C_p}{C_V}$$

Question 13

A gas expands adiabatically and quasi-statically. Which of the following statements is correct regarding the change in internal energy ($$\Delta E_{int}) $$and work ($$W$$)?

Accepted Answer

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

Question 14

In a free adiabatic expansion of an ideal gas, which of the following is true?

Accepted Answer

No work is done and the internal energy remains constant.

Question 15

Which of the following equations represents the adiabatic condition in terms of temperature and volume for an ideal gas?

Accepted Answer

$$TV^{\gamma-1}$$ = 	ext{constant}$$

Question 16

A gas is compressed adiabatically in a car engine cylinder. If the initial temperature is $$20^\circC $$and the final temperature after compression is $$600 K$$, what is the most likely reason for this temperature increase?

Accepted Answer

Work is done on the gas, increasing its internal energy.

Adiabatic Processes for an Ideal Gas

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