Question

For a sample of perfect gas when its pressure is changed isothermally from P_i to P_f, the entropy change is given by ______.

Options

• ΔS = RT In `(P_i/P_f)`

• ΔS = nR In `(P_f/P_i)`

• ΔS = nR In `(P_i/P_f)`

• ΔS = nRT In `(P_f/P_i)`

Answer 1

For a sample of perfect gas when its pressure is changed isothermally from P_i to P_f, the entropy change is given by ΔS = nR In `(P_i/P_f)`.

Explanation:

The quantity of heat that is reversibly transmitted to a system during a process is divided by the temperature at which the process takes place to determine the entropy change of that system.

∴  ΔS = `q_("rev")/T`

Now, q_rev for an isothermal change is given as:

q_rev = – w = nRT In `(P_i/P_f)`

∴  ΔS = `(nRT  "in"  (P_i/P_f))/T`

= nR In `(P_i/P_f)`