Which of the following scenarios would result in work being done by an ideal gas on its surroundings?

• A. The gas is compressed by an external force.
• B. The gas expands against a constant external pressure.
• C. The temperature of the gas is increased at constant volume.
• D. The gas is cooled at constant volume.

Answer: (B)

Verified step by step guidance

1. Recall the definition of work done by a gas in thermodynamics: work is done by the gas on the surroundings when the gas expands, pushing against an external pressure.
2. Understand that work done by the gas is given by the formula \(W = -P_{ext} \Delta V\), where \(P_{ext}\) is the external pressure and \(\Delta V\) is the change in volume of the gas.
3. Analyze each scenario: if the gas is compressed, \(\Delta V\) is negative, so work is done on the gas, not by the gas.
4. If the gas expands against a constant external pressure, \(\Delta V\) is positive, so the gas does work on the surroundings.
5. If the temperature changes at constant volume, \(\Delta V = 0\), so no work is done because volume does not change.