Fixed mass of an ideal gas contained in a $$24.63\,L$$   sealed rigid vessel at $$1\,atm$$  is heated from $$ - {73^ \circ }C$$  to $${27^ \circ }C.$$  Calculate change in gibb's energy if entropy of gas is a function of temperature as $$S = 2 + {10^{ - 2}}T\left( {J/K} \right):\,\left( {{\text{Use}}\,1\,atm\,L = 0.1\,kJ} \right)$$

Solution :
$$\eqalign{ & {\text{At constant volume}},\,\frac{{{P_1}}}{{{T_1}}} = \frac{{{P_2}}}{{{T_2}}} \cr & \Rightarrow {P_2} = 1 \times \frac{{300}}{{200}} = \frac{3}{2} \cr & {\text{and}}\,\,{V_1} = 24.63\,L \cr & {\text{for single phase}} \cr & \because \,\,dG = Vdp - SdT \cr & \Delta G = V\Delta P - \int {\left( {2 + {{10}^{ - 2}}T} \right)dT} \cr & = 1231.5 - 200 - \left( {\frac{{{{10}^{ - 2}} \times 50,000}}{2}} \right) \cr & = 781.5\,J \cr} $$