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Fluids
Heat capacity CV
The molar heat capacity of a gas is defined
as the amount of heat required to increase one mole of the gas
by a temperature of 1oC.
For a gas this quantity depends on the process.
When we consider an isochoric process
then the molar heat capacity is defined as
CV,
which is the heat capacity at
constant volume.
Hence, to heat n moles of an ideal gas
from temperature
T1
to temperature
T2
at a constant volume V,
we need an amount of heat equal to
Q1→2
= nCV(T2-T1)
In the previous page we found for the heat
Q1→2
which was needed
to increase the temperature of a quantity
of N molecules
from
T1
to
T2
at constant volume
V,
to be equal to
Q1→2
= 3(P2V-P1V)/2
By the use of the ideal-gas law that expression can be written as
Q1→2
= 3(nRT2-nRT1)/2
= 3nR(T2-T1)/2
Hence, we find for the specific heat
CV
the relation
CV = 3R/2
Notice, moreover, that, on comparing with the
expression
for
CP,
we find
CP
- CV = R
The latter relation is generally valid for
ideal gases.
A table on molar heat capacities can be found at
Hyperphysics.
heat engine