# Work done by ideal gas processes

Hello all,

In my physics textbook they discuss work done by ideal gas processes. The equation they give is Wgas = pΔV. I'm trying to figure it out if this is work done ON the gas by the surroundings, or work done BY the gas on surroundings.

From a previous chapter, they presented the conservation of energy equation as Ei + Wnet,ext = Ef. Work in this equation is the net, external work on the system, such that +W is work by the surroundings on the system, and -W is work by the system on the surroundings. It would seem from this preliminary chapter that we would be defining any W as work ON the system by surroundings.

However Wgas can't possibly be work done ON the gas, because if a gas is expanding, it supposedly has +Wgas even though it is doing work on the surroundings (therefore Wnet,ext should be negative). Could anybody confirm my thinking and does anybody know a good way to distinguish these two?

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DrClaude
Mentor
You pretty much have it. It all depends on the convention used, so if you take
$$W_\mathrm{gas} = p \Delta V$$
then ##W_\mathrm{gas} > 0## for work done by the gas (i.e., ##\Delta V > 0##).

In the energy equation
$$E_i + W_\mathrm{net,ext} = E_f$$
##W_\mathrm{net,ext} > 0## for work done on the gas. Therefore,
$$W_\mathrm{net,ext} = -W_\mathrm{gas} + W_\mathrm{other}$$

I must say that it is a strange convention: you usually would take the sign of ##W## to mean on/by directly. But it happens that depending on the situation, you would take one convention or the other depending on if the gas is the focus of attention or not. I know a textbook where the convention changes between two chapters, as it goes from looking at the properties of ideal gases to heat engines.

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Redbelly98
Staff Emeritus
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