Which of the following relationships represents the change of entropy of a perfect gas? 

1.

2.

3. 

4. 

Concept:

Entropy equations of a perfect gas:  

From the combined equation for first and second law:

First equation:

Tds = du + pdv 

For perfect gas, du = C_vdT

Pv = RT

      ----(1)

Second equation:

Tds = dh – vdP

For perfect gas, dh = C_pdT

      ----(2)

The ideal gas equation Pv = RT can be written as 

Taking differential on both sides 

Now putting the value of dT/T in eqn (1)

It is known that C_p = C_v + R 

      ----(3)