Page 76 - DJJ20063- Thermodynamics 1

DJJ20063- Thermodynamics 1

2.7 Relationship Between The Specific Heats

Let a perfect gas be heated at constant pressure from T1 to T2. With reference to the non-
flow equation Q = U2 – U1 + W, and the equation for a perfect gas

U2 – U1 = mCv(T2 – T1), hence,

Q = mCv(T2 – T1) + W

In a constant pressure process, the work done by the fluid is given by the pressure times

the change in volume, i.e. W = P(V2 – V1). Then using equation PV = mRT, we have
W = mR(T2 – T1)

Therefore substituting,
Q = mCv(T2 – T1) + mR(T2 – T1) = m(Cv + R)(T2 – T1)

But for a constant pressure process from equation 2.23,

Q = mCp(T2 – T1)

Hence, by equating the two expressions for the heat flow Q, we have
mCp(T2 – T1) = m(Cv + R)(T2 – T1)

Cp = Cv + R

Alternatively, it is usually written as

R = Cp - Cv (2.24)

2.8 Specific Heat Ratio ()

The ratio of the specific heat at constant pressure to the specific heat at constant volume
is given the symbol  (gamma),

C
i.e.  = p (2.25)
C v

Note that since Cp - Cv= R, from equation 3.16, it is clear that Cp must be greater than Cv

for any perfect gas. It follows therefore that the ratio Cp/Cv =  , is always greater than
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