Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature T_a = 27^ C, is enclosed in a metal cylinder of volume V₀ fitted with a frictionless piston. The gas is suddenly compressed to state b with volume V₀/3 . Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature 11^ C until the gas reaches the temperature of the water bath, which is de

Step-by-step solution

For state a : n = 10 , T_a = 27^ C = 300 K , P_a = 1 atm , V_a = V₀ . For a monoatomic gas, C_v = 3 2 R and = 5 3 . Process a b is a sudden compression, which is an adiabatic process. V_b = V₀ 3 Using T_a V_a^ -1 = T_b V_b^ -1 : T_b = T_a ( V_a V_b )^ -1 = 300 (3)^ 5/3 - 1 = 300 3^ 2/3 = 300 (9)^ 1/3 Given 9^ 1/3 = 2.08 , we get T_b = 300 2.08 = 624 K . Using P_a V_a^ = P_b V_b^ : P_b = P_a ( V_a V_b )^ = 1 (3)^ 5/3 = 3 3^ 2/3 = 3 2.08 = 6.24 atm . Thus, the pressure at state b is 6.24 times the atmospheric pressur