Consider a perfect gas contained in a cylinder and separated by a frictionless adiabatic piston into two sections A and B. All changes in B are isothermal; that is, a thermostat surrounds B to keep its temperature constant. There is 2.00mol of the gas molecules in each section. Initially T_A =T_B =300K, V_A =V_B =2.00dm³. Energy is supplied as heat to Section A and the piston moves to the right reversibly until the final volume of Section B is 1.00dm³. Calculate

(a) ΔS_A and ΔS_B,

(b) ΔA_A and ΔA_B,

(c) ΔG_A and ΔG_B,

(d) ΔS of the total system and its surroundings. If numerical values cannot be obtained, indicate whether the values should be positive, negative, or zero or are indeterminate from the information given. (Assume C_V,m =20JK⁻¹mol⁻¹.)