Using a compressor, I augment the pressure in a volume (using atmospheric air). I only measure the pressure inside. I now that the density will increase however, the temperature decreases. Can any one give a hint how can I calculate any of the two if the only known values are the volume and the pressure.
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A few clarifications on this thread in case anyone is reading in the future and is getting confused.
I know however, that the temperature did in fact change, hence it's not an adiabatic process.
That isn't really how an adiabatic process is defined. The temperature can change within a system (and often does) and it still be adiabatic. An adiabatic process is simply one where no heat is transferred across the system boundary. So if the compression of the gas is really quick, you can look at the state before and after compression and assume the system is adiabatic since not enough time will have passed for any meaningful amount of heat to transfer out of the system through conductive heat transfer.
Adiabatic refers to constant entropy
A constant entropy process is simply referred to as "isentropic".
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Normally when compressing a gas the temperature increases. If you assume adiabatic compression, the law is $PV^\gamma=k$, where $\gamma=\frac {C_P}{C_V}$ is the ratio of specific heats and is usually about $1.4$ for air. Then, as shown here $\frac {T_2}{T_1}=\left(\frac {P_2}{P_1}\right)^{\gamma-\frac 1\gamma}$ This assumes you don't leak heat to the walls, probably not such a good assumption.
Ross Millikan
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