Which is the correct expression that relates changes of entropy with the change of pressure for an ideal gas at constant temperature, among the following?

Options

A. `DeltaS=nRT" ln "(P_(2))/(P_(1))`
B. `DeltaS=T(P_(2)-P_(1))`
C. `DeltaS=nR" ln "((P_(1))/(P_(2)))`
D. `DeltaS=2.303nRT" ln "((P_(1))/(P_(2)))`

Answer

C

Explanation

From first law, `DeltaU=q-w`
`0=q-w` (for isothermal process)
`q=w=PdV`
`dS=(q)/(T)=(PdV)/(T)`
`dS=nR(dV)/(V)`
On integration, `DeltaS=nR" ln "((V_(2))/(V_(1)))`
`DeltaS=nR" ln "((P_(1))/(P_(2)))` Since, `P_(1)V_(1)=P_(2)V_(2)` according to Boyle's law.