Question

Question #779d2

Answer 1

Work done as the gas expands into a vacuum is zero. Zero does not have a sign.

Explanation:

When gas expands into vacuum we see that its pressure is zero.

We know that pressure of a gas is the force that its particles exert on the walls of the container divided by the area.
In a vacuum there is no container. As such the pressure is zero.

Mathematically stated
In vacuum, initially the temperature of the gas would be higher than the temperature of environment. Therefore, it would radiate energy and its final temperature would be `0K`.

From the gas equation
`PV=nRT`, for `T=0` we have
`PV=0`. As the volume of the gas can't be zero,therefore,
`P=0`.

This implies that from the given equation work done as the gas expands into a vacuum is zero. Zero does not have a sign.