Question:
Part A: Which of the following must be true about an ideal gas that undergoes an isothermal expansion? (There may be more than one correct choice.)
- A. No heat enters the gas.
- B. The pressure of the gas decreases.
- C. The internal energy of the gas does not change.
- D. The gas does positive work.
Options:
- A, C
- B, D
- A, B, C
- B, C, D
Answer:
The correct answer is: B, C, D
Explanation:
In an isothermal process, the temperature of the gas remains constant. Let’s evaluate each option based on the laws of thermodynamics and the properties of ideal gases:
A. No heat enters the gas – False
In isothermal expansion, the gas does work on its surroundings. Since the internal energy (ΔU) of an ideal gas depends only on temperature and the temperature is constant, ΔU = 0. According to the first law of thermodynamics:
ΔU = Q – W → 0 = Q – W → Q = W
This means that heat must enter the gas to compensate for the work done. Hence, statement A is incorrect.
B. The pressure of the gas decreases – True
From the ideal gas law: PV = nRT. In isothermal conditions, T and nR are constant. If volume V increases during expansion, pressure P must decrease. So, pressure decreases as the gas expands.
C. The internal energy of the gas does not change – True
The internal energy U of an ideal gas depends solely on temperature. Since temperature remains constant in isothermal processes, internal energy remains unchanged.
D. The gas does positive work – True
During expansion, the gas pushes against external pressure and performs work. Since it is expanding, the work is done by the gas, and thus, it’s considered positive work.
Conclusion:
The statements that are true for an ideal gas undergoing an isothermal expansion are:
- B: Pressure decreases
- C: Internal energy does not change
- D: Gas does positive work
Thus, the correct choice is: B, C, D