Half mole of an ideal gas ( = 5/3 ) is taken through a cycle abcda in a P - V diagram. The states are located at a(5000 cm ^3, 100 kPa ) , b(10000 cm ^3, 100 kPa ) , c(10000 cm ^3, 200 kPa ) , and d(5000 cm ^3, 200 kPa ) . Take R = 25 3 J K ⁻¹ mol ⁻¹ . Determine the amount of heat supplied in the processes ab and bc .

Step-by-step solution

Given for the ideal gas, = 5 3 . The molar heat capacities are: C_v = R - 1 = R 5 3 - 1 = 3 2 R C_p = R - 1 = 5 2 R From the P - V diagram, the states are: P_a = 100 kPa = 10^5 Pa , V_a = 5000 cm ^3 = 5 10⁻³ m ^3 P_b = 100 kPa = 10^5 Pa , V_b = 10000 cm ^3 = 10 10⁻³ m ^3 P_c = 200 kPa = 2 10^5 Pa , V_c = 10000 cm ^3 = 10 10⁻³ m ^3 Process ab is isobaric (constant pressure). The heat supplied is: Q_ ab = nC_p T = C_p R (nR T) = C_p R P V Q_ ab = 5 2 P_a (V_b - V_a) Q_ ab = 5 2 10^5 (10 10⁻³ - 5 10⁻³) Q_ ab = 5 2 10^