Page 73 - DJJ20063- Thermodynamics 1

DJJ20063- Thermodynamics 1

2.5 Specific Heat Capacity at Constant Volume (Cv)

The specific heat capacities of any substance is defined as the amount of heat energy

required to raise the unit mass through one degree temperature raise. In

thermodynamics, two specified conditions are used, those of constant volume and
constant pressure. The two specific heat capacities do not have the same value and it is

essential to distinguish them.

If 1 kg of a gas is supplied with an amount of heat energy sufficient to raise the

temperature of the gas by 1 degree whilst the volume of the gas remains constant, then

the amount of heat energy supplied is known as the specific heat capacity at constant

volume, and is denoted by Cv. The unit of Cv is J/kg K or kJ/kg K.

For a reversible non-flow process at constant volume, we have

dQ = mCvdT (2.19)

For a perfect gas the values of Cv are constant for any one gas at all pressures and

temperatures. Equations (2.19) can then be expanded as follows:

Heat flow in a constant volume process, Q12 = mCv(T2 – T1) (2.20)

Also, from the non-flow energy equation
Q – W = (U2 – U1)

mcv (T2 – T1) – 0 = (U2 – U1)
 (U2 – U1) = mCv(T2 – T1) (2.21)

i.e. dU = Q

Note:

In a reversible constant volume process, no work energy transfer can take place
since the piston will be unable to move i.e. W = 0.

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