# When does gas do more work: constant pressure or temperature?

• Sudikshya Pant
The isotherm will have a smaller area (and thus less work). At constant temperature, you have a curve that starts below the volume axis and rises to above the parallel line. The curve will have a greater area (and thus more work).In summary, the conversation discusses the comparison between the work done by a gas undergoing expansion at constant pressure and constant temperature. While the answer in the book states that the work done at constant temperature is greater, the mathematical solution suggests that the work done at constant pressure is actually greater. However, both cases will have different results due to the different areas under the pV diagram.
Sudikshya Pant
A quantity of ideal gas undergoes an expansion that doubles its volume. Does the gas do more work on its surroundings if the expansion is at constant pressure or at constant temperature?

The answer in the book says W at constant temperature gives a greater value for the given case.

But when I tried to solve it mathematically, I got greater value of W at constant pressure which is plain wrong. I don't understand where did I go wrong.

For constant pressure my result was:

W = p(2V-V) =pV = (nRT/V)*V =nRT

For constant temperature my result was:
W= nRT ln(2V/V) =nRT ln(2) =0.69 nRT

So, I got lesser value for constant temperature than constant pressure.

Where did I went wrong?

If both cases start out at the same pressure and volume (and temperature), then the constant pressure does more work.

I don't think you went wrong anywhere. If you draw a pV diagram of the two processes, starting at the same point, the area under each curve is the work done by the gas. At constant pressure, you have a line parallel to the volume axis while the isotherm drops below it.

Chestermiller

## 1. When does gas do more work: constant pressure or temperature?

Gas does more work at constant pressure, as the volume of the gas increases while the pressure remains constant, allowing it to exert a greater force on its surroundings.

## 2. How does the temperature affect the work done by gas?

The temperature of gas does not directly affect the work done, as work is dependent on the volume and pressure of the gas. However, changes in temperature can affect the volume and pressure, thus indirectly impacting the work done.

## 3. What is the formula for calculating work done by gas at constant pressure?

The formula for calculating work done by gas at constant pressure is W = PΔV, where W is work, P is pressure, and ΔV is change in volume.

## 4. Is there a limit to the work that gas can do at constant pressure?

Yes, there is a limit to the work that gas can do at constant pressure. This limit is determined by the initial and final volumes of the gas, as well as the pressure at which the gas is held constant.

## 5. Can gas do work at constant temperature?

Yes, gas can do work at constant temperature, but it is limited by the change in volume. This is because at constant temperature, the pressure of the gas will also change as the volume changes, resulting in a net work of zero.

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