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.

Wed Nov 26 17:12:00 EST 1997