One mole of a monoatomic ideal gas undergoes the process A B in the given p-V diagram. The molar heat capacity for this process is

Step-by-step solution

aligned W_ A B & = Area under p-V diagram & =4 V₀ 3 p₀+ 1 2 4 V₀ 3 p₀=18 p₀ V₀ aligned aligned U & =n C_V T & =1 3 2 R (T_B-T_A ) & = 3 2 R ( 30 p₀ V₀ R - 3 p₀ V₀ R ) & = 81 2 p₀ V₀ aligned Thus, Q_ A B = W_ A B + U_ A B =18 p₀ V₀+ 81 2 p₀ V₀= 117 2 p₀ V₀ Molar heat capacity, C= Q n T = 117 p₀ V₀ / 2 30 p₀ V₀ R - 3 p₀ V₀ R = 117 p₀ V₀ / 2 27 p₀ V₀ R = 13 R 6