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.