Question 1

Which of the following best describes the difference between an ideal gas and a real gas, as illustrated in the provided diagrams?

Accepted Answer

Ideal gases have molecules with no volume and no intermolecular forces, while real gases have molecules with finite volume and experience intermolecular attractions.

Question 2

Given the van der Waals equation $$\left( p + \frac{an^2$}{V^2$} \right)(V - nb) = nRT$$, what does the term $$nb$$ account for?

Accepted Answer

The finite volume occupied by the gas molecules themselves.

Question 3

A gas in a cylinder with a moveable piston is heated while the piston is allowed to move freely. Which of the following state variables must change as a result?

Accepted Answer

At least one of pressure, volume, or temperature must change.

Question 4

Which of the following is the correct form of the ideal gas law?

Accepted Answer

$$pV = nRT$$

Question 5

If a gas behaves ideally, which of the following statements is true about the relationship between pressure and volume at constant temperature?

Accepted Answer

Pressure is inversely proportional to volume.

Question 6

In the context of thermodynamics, what is meant by a 'diathermal' wall?

Accepted Answer

A wall that allows heat (energy) to pass through but not matter.

Question 7

Which of the following is NOT a state variable in thermodynamics?

Accepted Answer

Heat

Question 8

A sample of gas is compressed at constant temperature. According to the ideal gas law, what happens to the pressure?

Accepted Answer

It increases.

Question 9

Which correction in the van der Waals equation accounts for the intermolecular attractions in a real gas?

Accepted Answer

$$\frac{an^2$}{V^2$}$$

Question 10

A gas sample contains 2 moles of a substance with a molar mass $$M = 28 \ \mathrm{g/mol}. $$What is the total mass of the gas?

Accepted Answer

$$56 \ \mathrm{g}$$

Question 11

Which of the following best describes an 'open' thermodynamic system?

Accepted Answer

A system that can exchange both matter and energy with its surroundings.

Question 12

If the pressure, volume, and temperature of a gas are related by $$pV = nRT$$, what happens to the volume if the temperature is doubled at constant pressure and number of moles?

Accepted Answer

The volume doubles.

Question 13

Which of the following is a limitation of the ideal gas law?

Accepted Answer

It does not account for intermolecular forces or the finite volume of molecules.

Question 14

A real gas deviates from ideal behavior at high pressures because:

Accepted Answer

The volume of the gas molecules becomes significant compared to the container volume.

Question 15

Which of the following statements about the gas constant $$R is $$correct?

Accepted Answer

$$R$$ has the same value for all gases.

Question 16

A gas is contained in a cylinder with a moveable piston and diathermal walls. If the system is compressed rapidly so that no heat escapes, what type of process is this?

Accepted Answer

Adiabatic

Question 17

Which of the following best explains why the van der Waals equation predicts lower pressures than the ideal gas law at the same $$V$$, $$n$$, and $$T$$?

Accepted Answer

Intermolecular attractions reduce the effective pressure exerted on the container walls.

Question 18

If a gas sample is described by the van der Waals equation, which of the following changes would increase the deviation from ideal gas behavior?

Accepted Answer

Increasing the pressure.

Question 19

Which of the following is a correct statement about state variables in thermodynamics?

Accepted Answer

They describe the current state of a system and are not independent of each other.

Question 20

A gas is described by the van der Waals equation. If the attractive forces between molecules are increased (larger $$a$$), what is the effect on the pressure at a given $$V$$, $$n$$, and $$T$$?

Accepted Answer

The pressure decreases compared to the ideal gas prediction.

Equations of State and the Kinetic Theory of Gases

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