Page 54 - Instant notes

Physical Chemistry 40

temperature of a system is proportional to the amount of heat which is input into it, and
they are related through the heat capacity, C:
dq=C.dT (infinitesimal change)
or q=C∆T (finite change when C is temperature independent)

The heat capacity of a substance depends upon whether the substance is allowed to
expend energy in expansion work or not, and hence there are two possible heat capacities,
the constant volume heat capacity, C v, which is the heat capacity measured at constant
volume, and the constant pressure heat capacity, C p, which is measured at constant
pressure. The two are approximately identical for solids and liquids, but for gases they
are quite different as energy is expended in volume expansion work. They are related
through the formula:
C p=C v+nR

Since, at constant volume, the heat supplied is equal to the change in internal energy, δU,
it is possible to write:
∂U=C v ∂T or ∆U=C v ∆T

when C v is independent of temperature.
The molar heat capacity, C m is the heat capacity per mole of substance:
C m=C/n

The larger the value of C m the more heat is required to accomplish a given temperature
rise.