# Ideal gas law, pressure increase and temperature

If I had a container, full with air, and I suddenly decreased the volume of the container, forcing the air into a smaller volume, will it be considered as compression, will it result in an increase in temperature, and why?

P.S: the container is strong enough to bear high pressure and not to explode.

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Possible duplicate: physics.stackexchange.com/q/17948/2451 –  Qmechanic Sep 15 '12 at 9:58

Yes, it is compression and yes, it will heat up the gas.

If there's no heat exchange between the gas and the container (or the environment), we call it an adiabatic process. For an adiabatic process involving an ideal gas (which is a very good approximation for most common gases), $pV^\gamma$ is constant where $\gamma$ is an exponent such as $5/3$. Because the temperature is equal to $T=pV/nR$ and $pV/pV^\gamma=V^{1-\gamma}$ is a decreasing function of $V$, the temperature will increase when the volume decreases.

Macroscopically, the heating is inevitable because one needs to perform work $p\,|dV|$ to do the compression, the energy has to be preserved, and the only place where it can go is the interior of the gas given by a formula similar to $(3/2)nRT$.

Microscopically, the gas molecules are normally reflected from the walls of the container with the same kinetic energy. However, the molecules that hit the wall moving "against them" during compression will recoil with a greater velocity. If one calculates the average energy gain for the molecules, he gets the same temperature increase as one that follows from the macroscopic calculation.

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in fact there is heat exchange with the environment , will it still heat up? if yes will the heat exchange with the environment will result in thermal equilibruim? thank you very much –  Abdelrahman Esmat Sep 15 '12 at 10:51
If heat exchange is allowed, the objects in contact always converge towards thermal equilibrium. For compression, some contact will mean that the heating will simply not be as fast, it will be something in between the adiabatic process above in which it's warming pretty quickly and isothermal process in which the temperature is fixed. –  Luboš Motl Sep 15 '12 at 12:17
is there any way to calculate the temperature increase? what's the name of this kind of compression? –  Abdelrahman Esmat Sep 15 '12 at 19:33
Practical applications of that principle include the diesel engine (which requires no spark plug because of it) and the fire piston (a device to light fire with in absence of matches etc). –  Hanno Fietz Dec 2 '12 at 18:24