Q: Which equation describes the relationship between pressure and volume in a reversible adiabatic process for an ideal gas?

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

Question 1

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

Accepted Answer

The process occurs at constant volume, and all energy added as heat increases the internal energy.

Question 2

For an isothermal expansion of an ideal gas, which equation correctly gives the work done by the gas?

Accepted Answer

$$ W = nRT \ln \frac{V_2$}{V_1$} $$

Question 3

In an adiabatic process for an ideal gas, which of the following statements is true?

Accepted Answer

No heat is transferred into or out of the system.

Question 4

A gas is compressed adiabatically and reversibly. What happens to its temperature and why?

Accepted Answer

The temperature increases because work is done on the gas and no heat escapes.

Question 5

Which equation describes the relationship between pressure and volume in a reversible adiabatic process for an ideal gas?

Accepted Answer

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

Question 6

During an isobaric expansion, which of the following is true for the work done by the gas?

Accepted Answer

$$ W = p (V_2$ - V_1$) $$

Question 7

A laboratory Dewar flask is used to store liquid nitrogen. Which thermodynamic process does this device best approximate for the contents?

Accepted Answer

Adiabatic

Question 8

When the cork is popped from a champagne bottle, the rapid expansion of gas is nearly adiabatic. What is a direct observable consequence of this process?

Accepted Answer

The temperature of the gas decreases, causing water vapor to condense and form a cloud.

Question 9

For a monatomic ideal gas, what is the value of $$ \gamma  ($$the ratio of heat capacities)?

Accepted Answer

$$ \gamma = 1.67 $$

Question 10

Which of the following correctly expresses the change in internal energy $$ \Delta U $$ for an isochoric process?

Accepted Answer

$$ \Delta U = Q $$

Question 11

In which process does the internal energy change equal the negative of the work done by the system?

Accepted Answer

Adiabatic

Question 12

A gas undergoes a reversible adiabatic expansion from $$ (p_1$, V_1$)  to$$ $$ (p_2$, V_2$) . $$Which equation gives the final temperature $$ T_2$  in $$terms of the initial temperature $$ T_1$ $$ and volumes?

Accepted Answer

$$ T_2$ = T_1$ \left( \frac{V_1$}{V_2$} \$$right)^{\gamma - 1}$$ $$

Question 13

Which of the following is true for the work done by an ideal gas in a reversible adiabatic process?

Accepted Answer

$$ W = \frac{p_2$ V_2$ - p_1$ V_1$}{1 - \gamma} $$

Question 14

Which process is represented by a vertical line on a pV-diagram?

Accepted Answer

Isochoric

Question 15

Why are adiabatic curves steeper than isothermal curves on a pV-diagram for an ideal gas?

Accepted Answer

Because $$ \gamma \u003e 1 $$ for all ideal gases.

Question 16

Which of the following is a real-life example of an adiabatic process?

Accepted Answer

Compressing air rapidly in a bicycle pump.

Question 17

For a diatomic ideal gas, what is the value of $$ C_V  in $$terms of $$ R $$?

Accepted Answer

$$ C_V = \frac{5R}{2} $$

Question 18

Which process is best described by the equation $$ Q = 0 $$?

Accepted Answer

Adiabatic

Question 19

In which process does the pressure of an ideal gas remain constant while the volume and temperature change?

Accepted Answer

Isobaric

Work, Heat, and Internal Energy in Thermodynamic Processes

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