Question

One mole of helium gas, initially at STP (p₁ = 1 atm, T₁ = 0°C), undergoes an isovolumetric process in which its pressure falls to half its initial value. The work done by the gas is:

• A. 101 J
• B. 51 J
• C. 23 J
• D. 0 J

Hint:

In an isovolumetric process, the volume remains constant, meaning no work is done by the gas.

Answer 1

The Correct Option is D

In this problem, we need to determine the work done by one mole of helium gas during an isovolumetric process.

First, let's understand the key term:
Isovolumetric Process: This is a thermodynamic process in which the volume remains constant. Since the volume does not change, no work is done by or on the gas during the process. Work done is given by the formula:
W = P∆V
where W is the work done, P is the pressure, and ∆V is the change in volume.

Since the process is isovolumetric (∆V = 0):
W = P * 0 = 0

Therefore, the work done by the gas is simply 0 J.

Answer 2

This question is really testing whether the meaning of isovolumetric is understood, since the actual numbers (pressure, moles, temperature) barely matter once that word is recognised.

1. 101 J: A nonzero answer like this would only make sense if the gas's volume actually changed during the process, letting it push against something or be pushed on. That is not what isovolumetric describes.
2. 51 J: Same issue as the first option: any nonzero value assumes some volume change happened, which contradicts the constant-volume condition stated in the question.
3. 23 J: Again, a nonzero figure implicitly assumes the gas moved a piston or expanded against pressure, which cannot happen if the container's volume is fixed throughout.
4. 0 J: Work done by a gas is defined as the pressure times the change in volume it undergoes. In an isovolumetric process the volume never changes, so the change in volume is exactly zero, making the work done exactly zero as well, no matter how much the pressure itself changes.

Work only gets done when a gas actually pushes its boundary outward or inward, changing its volume. Since this process is defined as isovolumetric, that boundary never moves, so there is nothing for the gas to push against.

So the correct answer is 0 J.