Application of energy equation to an ideal gas

For an ideal gas in a closed system, equation of state is

1.160

1.161

1.162

U does not change with V at constant temperature.
Further, applying Theorem 2,

1.163

Hence,

1.164

Since,

1.165

From Eqs.(1.162) and Eq. (1.165) it is clear that U is neither a function of V nor a function of P at constant temperature. Only possibility is that internal energy is a function of temperature only.

For an open system

dH = Tds + Vdp

1.166

From second T - dS relation,

1.167

Now,

1.168

Let, H = H(T, p)

Hence,

1.169

Comparing Eq. (1.167) and Eq. (1.168),

1.170

Now,

1.171

For an ideal gas

1.172

Hence,

1.173

∴ H does not change with p while temperature remaining unchanged.

From, we can infer that

∴ H does not change with V while temperature remaining unchanged.