Question

 Two systems A and B are arranged so that their total volume is constant, but their individual volumes can change. Calculate the standard deviation of fluctuations in the volume in system A for constant energy. (Hint: see section 4.5 for the analogous calculation of the fluctuation ill energy.)

Answer 1

$$(\frac {\delta S}{\delta U_A})_{U_A=U_A^*}=\frac{S(U_A)-S(U_A^*)}{(U_A-U_A^*)}$$