# Work done by gas in vacuum

#### nil1996

I learnt that work done by gas is zero when a gas expands in vacuum.
But the volume and pressure of the gas change.Then how work done by gas is zero?

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#### ShayanJ

Gold Member
The point is,in a vacuum,there is nothing that the gas can do work on!
Also,there is nothing that the gas has to overcome its pressure to expand,so the work it does in expanding is zero.
For another thing,pressure of a gas is the force that its particles exert on the walls of their container divided by the area.But in a vacuum there is no container,so the pressure is zero.
For another reasoning leading to pressure being zero.In a vacuum,whatever the temperature of the gas is,its higher than the temperature of the environment,so it radiates energy until its temperature reaches 0K(classically). And using $PV=nRT$,we will have $PV=0$. But the volume of the gas can't be zero,so P=0. Using the ideal gas equation is justified because in a vacuum,the only force on the particles is the force by other ones. There is also diffusion to the directions leading to outside of the gas because the concentration decreases in those directions and I think the diffusion flux is dominant so the gas expands and it will behave like an ideal gas with a very good approximation.

#### nil1996

Why cant we say that in vacuum some negative pressure is doing work on the gas?

#### ShayanJ

Gold Member
Why cant we say that in vacuum some negative pressure is doing work on the gas?
1-Its not well-defined,maybe not defined at all!
2-Pressure is casued by force.If we consider the gas as one entity,then there is only one thing in our system,the gas.So there can be no force,and so,no pressure.
3-I just proved that the pressure of the gas is zero in the situation you described.
4-There is no need to,we have a satisfactory explanation!

#### nil1996

thanks for that explanation

#### jartsa

I learnt that work done by gas is zero when a gas expands in vacuum.
But the volume and pressure of the gas change.Then how work done by gas is zero?

Pressure decreases, but we have a bigger tank of gas.

(for example when a small gas tank explodes inside a large vacuum tank)

5 liters of gas in 10 atm has as much pneumatic energy as 10 liters of gas in 5 atm

"Work done by gas in vacuum"

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