Answer to Question #94264 in Physical Chemistry for Abhishek

Question

starting from the definition of Helmholtz free energy (A) derive relations for its variation with
(1) temperature at a constant volume and

(2) volume at a constant temperature.

Answer 1

Helmholz free energy is given by:

$A=H-TS\\where\ \\U=internal\ energy\\T=temprature\\S=entropy\\A=helmholz\ free\ energy$

$Or,\\\ \ \ \ \ \ \ dA=dU-d(TS)\\\ \ \ \ \ \ \ dA=TdS-PdV-(TdS+SdT)$

$\ \ \ \ \ \ \ dA=-PdV-SdT\ \ \ \ \ \ \ .....\ \ \ \ (a)\\$

$(2)\ At\ constant\ temprature:SdT=0\\So,\ dA=-PdV\ \ \\\\(1)\ At\ constant\ volume:\ PdV=0\\So,\ dA=-SdT$