How work is done on an ideal gas?

[jerry0696]

Consider a system of volume V and pressure P ,if i add molecules of gases in the system while keeping its volume constant and not providing any energy nor absorbing energy from the system ,its pressure will increase and so does its temperature
Why does the temperature increase?
More molecules means more collision but the collisions are perfrctly elastic so it doesn't make any difference isn't it?
And for the temperature to increase work has to be done on the gas but how work is done on a fixed volume of gas?

 

[Nugatory]

And for the temperature to increase work has to be done on the gas but how work is done on a fixed volume of gas?

To add the molecules of gas, you had to push them into the container against the pressure of the gas already there. That pushing did work on them.

The temperature increase comes from increasing the average kinetic energy of the gas molecules as you pushed on them. The elastic nature of the collisions between the molecules just means that the kinetic energy of the molecules, both what they started with and what you added by pushing more molecules in, remains as kinectic energy.

 

[WannabeNewton]

You can't add molecules to the ideal gas keeping volume constant without changing its energy. It has a non-zero chemical potential.