A polyatomic molecule, for which C_V=3R and Cₚ=4R where R is the gas constant, goes from the phase-space point A(P_A=10⁵ Pa, V_A=4×10⁻⁶ m³) to the point B(P_B=5×10⁴ Pa, V_B=6×10⁻⁶ m³) and then to the point C(P_C=10⁴ Pa, V_C=8×10⁻⁶ m³). A to B is an adiabatic path and B to C is an isothermal path. T…

Question

A polyatomic molecule, for which C_V=3R and Cₚ=4R where R is the gas constant, goes from the phase-space point A(P_A=10⁵ Pa, V_A=4×10⁻⁶ m³) to the point B(P_B=5×10⁴ Pa, V_B=6×10⁻⁶ m³) and then to the point C(P_C=10⁴ Pa, V_C=8×10⁻⁶ m³). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is

Accepted Answer

(3) 450R(ln 4-ln 3). A to B is adiabatic, so Q_AB=0. B to C is isothermal, so Δ U=0 there and all the heat becomes work: Q_BC=nRT_B ln (V_C)/(V_B)=nRT_B ln 8/6=nRT_B ln 4/3. Per mole, with the temperature of the isotherm taken as 450 K, Q=450R ln 4/3=450R(ln 4-ln 3). The printed state values give P_BV_B/R=0.3/R K rather than 450 K, so the data and the key do not sit together. Listed in DEFECTS.md.

Step-by-step solution

Why the other options are wrong