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An adiabatic process is one in which no heat flows to or from our system and hence

Sometimes we say that the system is thermally isolated but this condition does not mean that temperature is constant. In fact all the thermodynamic variables P, V, and T change in an adiabatic process. From the first law we can immediately write

For the ideal gas the left side can as allays be written in terms of the isochoric specific heat so we have

From the first law of thermodynamics and the equation of state for an ideal gas it can be shown that

for an adiabatic process. In this expression

Thus given knowledge of the thermodynamic state at the beginning of the adiabatic process and one thermodynamic variable in the final state we can calculate the other thermodynamic variables of the final state using a combination of Eq. 26. For example if we know the initial volume and temperature and the final volume then we can get the final temperature by inserting the equation of state in Eq. 26 to get

From Eq. 27 we see that and hence a compression () leads to a rise in temperature. We have a demo experiment which clearly illustrates this result. You experience this heating effect in everyday life when you pump the tires of a bike with a manual pump. The pump gets hot not because of friction but because you are continuously performing semi-adiabatic compressions of the gas which heats and in turn heats up the pump for you to feel. We see that the smaller , the greater will be and the greater in turn will be the heating caused by an adiabatic compression.

Collin Broholm
Wed Nov 26 17:12:00 EST 1997