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

A. `DeltaS= nRln((p_(f))/( p_(i)))`
B. `DeltaS= nRln((p_(i))/( p_(f)))`
C. `DeltaS= nRTln((p_(f))/( p_(i)))`
D. `DeltaS= nRTln((p_(i))/( p_(f)))`

Answer

b

Explanation

For n moles of an ideal gas undergoing reversible expansion when temperature changes from`T_(1)` to`T_(2)`and pressure changes from `p_(1)` to `p_(2)`, entropy change is given by
`DeltaS = n C_(p) ln. (T_(2))/(T_(1)) + nRln. (P_(1))/(P_(2)) ` ( Refer to page) or `DeltaS = nC_(p)ln. (T_(f))/(T_(i))+ nRTln. (p_(i))/(p_(f))`
For isothermal expansion,
`T_(i) = T_(f)` so that `ln. (T_(f))/(T_(i)) = ln 1= 0`. Hence, `DeltaS = nR ln. (p_(i))/( p_(f))`