(i) Define first and the second law of thermodynamics in the combined form.
(ii)
(a) Write an expression for the entropy change of an ideal gas for isothermal change.
(b) Write an expression for entropy change for an ideal gas for isobaric change.

(iii) Calculate the maximum work obtained when 0.75 ml of an ideal gas expands isothermally and reversibly at 27°C from a volume of 15L to 25L.

Solution

(i) The energy of the universe is constant but the entropy of the universe is continuously increasing and tends to a maximum.
(ii)
(a)
$space increment straight S space equals space 2.303 space straight R space log space straight V subscript 2 over straight V subscript 1 space space space space space equals 2.303 space straight R space log space straight P subscript 1 over straight P subscript 2$
$left parenthesis straight b right parenthesis space space increment straight S space equals space 2.303 space straight C subscript straight p log space straight T subscript 1 over straight T subscript 2$
$left parenthesis iii right parenthesis space straight w space equals space 2.303 space nRT space log space straight V subscript 2 over straight V subscript 1$
Substituting the values, we have,
$straight w space equals space 2.303 space space cross times space 0.75 space cross times space 8.314 space cross times space 300 space log space 25 over 15 space space space space space equals space 955.5 space straight J$