Question

At constant temperature and volume, helmholtz free energy is shown by :

• A. $dA=TdS$
• B. $dA=U+dTS$
• C. $dA=-TdS$
• D. $dA=dAdS$

Answer 1

The correct option is C $dA=-TdS$

Helmholtz free energy is given by $A=U-TS$ where U=internal energy, T=temperature, S=entropy

$△A=△U-T△S-△TS$

At constant temp. $△T=0$

From 1st law: $dU=dW+dq$

At constant temperature and volume, $dW=0$

$dU=dq$

Since temp remain constant i.e. $△T=0$

It is an isothermal process.

Hence internal energy is zero.

So $△A=-T△S$

or $dA=-T△S$