# Pressure and Temperature

If there is a cylinder filled with gas and a piston compresses the volume to 1/2 the size, the pressure increases to twice the original pressure. Why does the temperature go up? Is it because PV=nRT only works for ideal gasses, and the non-ideal gasses go up in temperature? Thanks.

How does the volume go down?

(Does the piston drive forcefully into the gas, accelerating many individual molecules? Do you drive the piston infinitesimally slowly? Do you just wait until no molecules happen to be in part of the cylinder, and then close that part? Are you thinking of a big effect, occurring for all gases, or a small effect like deviation from the ideal gas law?)

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Triber, was this a homework question? (It sounded to me like it should have been moved only to the classical+thermodynamics forum otherwise.. I wonder if there is a way to know who moved particular threads and why?)

Andrew Mason
Homework Helper
If there is a cylinder filled with gas and a piston compresses the volume to 1/2 the size, the pressure increases to twice the original pressure. Why does the temperature go up? Is it because PV=nRT only works for ideal gasses, and the non-ideal gasses go up in temperature? Thanks.
No. Temperature goes up for all gases. It is a matter of energy. When you compress a gas you do work on the gas. If it is adiabatic (with no heat flow into or out of the gas), the temperature has to increase because the work is an input of energy into the gas.

That is just the first law:

dQ = dU + PdV.

Since dQ = 0, dU = -PdV .

And since $dU = nC_vdT$, $dT = -PdV/nC_v$

AM