A quasi-static cycle of a monoatomic ideal gas contains an isothermal process ( ab ) , followed by an isochoric process ( bc ) and an adiabatic process ( ca ) as shown in the figure. The volumes of the gas are V₁ and V₂ at a and b , respectively. If the cycle has heat input Q_ in and output Q_ out , then the efficiency of the cycle is defined as = Q_ in - Q_ out Q_ in . The correct statement(s) is/are: [Given: 2 0.7

Step-by-step solution

For the monoatomic ideal gas, = 5 3 . Process ab is isothermal, so T_a = T_b and V_a = V₁ , V_b = V₂ . Process bc is isochoric, so V_b = V_c = V₂ . Process ca is adiabatic, so T_c V_c^ -1 = T_a V_a^ -1 . T_c V₂^ 2/3 = T_a V₁^ 2/3 T_c = T_a ( V₁ V₂ )^ 2/3 . If V₂ V₁ = 8 , T_c = T_a ( 1 8 )^ 2/3 = T_a 4 T_a = 4 T_c . Thus, statement (C) is correct. Heat absorbed in isothermal process ab is Q_ ab = nRT_a ( V₂ V₁ ) . For V₂ V₁ = 8 , Q_ ab = nRT_a (8) = 3nRT_a 2 3 0.7 nRT_a = 2.1 nRT_a . Heat released in isochoric proce