# Example 2.5: Entropy rise in a ideal gas expansion

A diatomic ideal gas, available at 0.5 MPa and 300 K, is expanded continuously in an adiabatic process through a valve. The outlet pressure is atmospheric pressure. What is the state of the gas at the outlet and what is the rate of entropy increase if flow is 1 mol/s.

## Analysis:

No work is done during expansion, nor is heat exchanged. Hence, according to the first principle this is an isenthalpic expansion (). The properties to be calculated are h (PH calculation) and s (explicitly asked for) at the inlet and the outlet of the valve (the differences are looked for, which means that no reference state is required). The exit state must be defined using the first law of thermodynamics.

The component is an ideal gas and consequently the phase concerned is only vapour.

## Solution:

At the inlet, T and P are known, so enthalpy is calculated. At the outlet, P and H are known, so temperature is obtained.

With an ideal gas, there is no change in temperature during expansion (the Joule Thomson coefficient is zero). In their experiment of 1856, P. Joule and W. Thomson observed a small decrease in temperature using air, indicating clearly that is not exactly an ideal gas.

For the change of entropy, the same reasoning applies:

Hence, the rate of increasing entropy will be: