# Power To Compress Ideal Gas In A Piston

I am familiar with isothermal and adiabatic ideal gas compression problems where a force is exerted on a piston of area A to move it some displacement in order to calculate work done. However I am looking for how to calculate the power needed to move the piston head and compress the gas.

In my actual problem I have water entering one side of a piston at pressure Pw and flow rate Qw. The other side of the piston is filled with air at Pa.

I know the friction resistance of the piston seals, I know the piston mass, I know the force applied to piston by water pressure, and I know the gas properties. I would like to know how to find how long it takes for the force to compress the gas down and equalize the gas pressure with the force exerted. I believe this would be a power equation where P=W/t?

• Could you please clarify this comment? Are you just defining P= integral of (F*v) dt? Commented Sep 28, 2022 at 17:31
• Whoops! I misspoke. Sorry about that. Commented Sep 28, 2022 at 17:34
• How do you know that the power would be constant? It would not. Commented Sep 28, 2022 at 20:44
• I don't think it will be, I expect it to increase exponentially with time as the gas pressure approaches the water pressure. Commented Sep 29, 2022 at 11:38