AP EAMCET202120 Aug 2021Morning ShiftPhysicsThermodynamicsActual
For a monoatomic ideal gas following the cyclic process A B C A shown in the U vs ρ plot, identify the incorrect option:
Options
- AMolar heat capacity of the process AB is R 2
- BHeat is rejected by the system in path BC
- CMolar heat capacity for the process BC is 2 R 3
- DWork done by the system in the process CA is 2 U 0 3 ln 4
Correct answer
C. Molar heat capacity for the process BC is 2 R 3
Step-by-step solution
The internal energy of a system is a function of temperature only, i.e., U ∝ T Density is inversely proportional to volume, ρ ∝ 1 V So, for process AB, slope is constant, therefore, U 0 ρ 0 = T 1 V ⇒ T V = constant,  using ideal gas equation, T V = P V n R V ⇒ P V 2 = constsnt   Therefore, AB is a polytropic process, P V m = constant   of polytropic index 2 . For a monoatomic gas, C V = 3 2 R So, the molar heat capacity for a polytropic process is, C = C V