Thermodynamics conceptual question(for advanced people)?

[StarDust563]

If you compress a gas in a piston(a monoatomic perfect gas for instance), what is the equation that gives you the temperature of the gas or amount of heat introduced in the gas vs the volume of the gas?
And what is the ratio of energy that is transformed into heat vs into pressure? Is it constant through compression?

thanks a lot

 

[Andrew Mason]

If you compress a gas in a piston(a monoatomic perfect gas for instance), what is the equation that gives you the temperature of the gas or amount of heat introduced in the gas vs the volume of the gas?
And what is the ratio of energy that is transformed into heat vs into pressure? Is it constant through compression?

If this is an adiabatic compression (no heat flow into or out of the gas), then:

$$T_fV_f^{\gamma-1} = T_iV_i^{\gamma-1} = \text{Constant}$$

If heat is added, you have to know the heat flow and the work done by/on the gas and use the first law:

$$\Delta U = nC_v\Delta T = \Delta Q - W$$ where W is the work done by the gas (which is the negative of the work done on the gas - ie. in compressing the gas)

AM