Pressure in a piston cylinder assembly when both volume and temperature change

[Marts12]

I have a problem in relation to the pressure in a closed piston and cylinder assembly, I know the compression ratio and want to work out the pressure when the volume is at its lowest, boyles law only seems to works if the temperature remains constant but I know that as the piston moves and the volume becomes less the temperature will increase, how to I compensate for this in my calculations to work out pressure if both volume reduces and temperature increases?

 

[Ken G]

If you want to constrain two different things (like T and P), you need more than one equation. One equation will be the "ideal gas law" (a generalization of Boyle's law), but that isn't enough by itself. You also need to know something about what heat is doing-- is heat escaping when you compress, or is it all being trapped? Here you need the "first law of thermodynamics", to account for what work and heat are doing to the gas. There is a simple equation for work, but you also need to know what the heat is doing. The simplest thing is to keep the heat bottled in by "insulating" the piston, and then the result is "adiabatic" (use the first law of thermodynamics with zero heat exchange, and then track the work and the ideal gas law to get P and T). It's a little bit of an operation, but it is a very standard problem, you can see examples if you look up "adiabatic expansion."

 

[Marts12]

Thank you Ken G