KVPY2010PhysicsKinetic Theory of Gases
An ideal gas with constant heat capacity C _ V = 3 2 n R is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle-
Options
- AThe efficiency is given 1- P₁ V₁ P₂ V₂
- BThe efficiency is given by 1- 1 2 P ₁ ~V ₁ P ₂ ~V ₂
- CNet heat absorbed in the cycle is ( P ₂- P ₁ ) ( V ₂- V ₁ )
- DHeat absorbed in part AC is given by 2 ( P ₂ ~V ₂- P ₁ ~V ₁ )+ 1 2 ( P ₁ ~V ₂- P ₂ ~V ₁ )
Correct answer
B. The efficiency is given by 1- 1 2 P ₁ ~V ₁ P ₂ ~V ₂
Step-by-step solution
array l C _ V = 3 2 R , C _ P = C _ V + R = 5 R 2 f =3 ~W = 1 2 ( ~V ₂- V ₁ ) ( P ₂- P ₁ ) array For BA Q=n C p T=n ( 5 2 R ) T= 5 2 (P₁ V₁-P₂ V₂ ) For AC Q_ A C = 1 2 (P₁+P₂ ) (V₂-V₁ )+n C_ V T now n Cv T = 3 2 ( P ₂ ~V ₂- P ₁ ~V ₁ ) now = W Q = 1 2 (V₂-V₁ ) (P₂-P₁ ) 1 2 (P₁+P₂ ) (V₂-V₁ )+ 3 2 (P₂ V₂-P₁ V₁ ) using formula for heat we can calculate heat absorbed in AC .