Question

A gas goes from the start (state i) to the end (state f), where the end has less pressure. Which of these correctly puts the work done (W) in order?

a) Wi > Wf

b) Wi = Wf

c) Wi < Wf

Answer 1

c) Wi < Wf

Step-by-step explanation:

When a gas undergoes a process from state i to state f and the end state (f) has less pressure than the initial state (i) the work done (W) is given by the equation W = PΔV where P is the pressure and ΔV is the change in volume. Assuming the volume increases during the process the work done is positive. Now since the final state has less pressure, the gas has done more work against the external pressure leading to a greater absolute value for the work done. Therefore, Wi (work done at the initial state) is less than Wf (work done at the final state). This relationship is expressed as Wi < Wf.

To elaborate as the gas expands it does work against the external pressure. The work done is proportional to the pressure and the change in volume. In this scenario the lower final pressure implies that the gas is working against a smaller opposing force, allowing it to do more work. Mathematically,
`W = PΔV, where ΔV` is the volume change. With lower pressure at the final state Wf > Wi. Hence, the correct choice is c) Wi < Wf.

In conclusion the relationship between the work done at the initial and final states is determined by the change in pressure and volume during the process. The given conditions lead to the conclusion that the work done at the initial state is less than the work done at the final state making option c) the correct choice.