Engineering
Physics
Degree of Freedom Internal Energy of Gas and Specific Heat Capacity of Gases
Thermodynamics
Cyclic Processes
Question

The P-V Diagram shown here is a cycle performed on an ideal monoatomic gas. Of the three processes, one is isothermal and one is an adiabatic process. Match the description of each process with the process

  

Column-I Column-II
(A) 1 – 2 (P) No work is done during this process
(B) 2 – 3 (Q) Work is done by the gas during this process
(C) 3 – 1 (R) Work is done on the gas during this process
  (S) Internal energy of the gas changes during this process
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Solution
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In a P-V diagram, work done is the area under the curve. For an ideal monoatomic gas, internal energy U = (3/2)nRT.

Process 1→2: Volume decreases at constant pressure. Work is done on the gas (R). Temperature decreases, so internal energy decreases (S).

Process 2→3: Volume is constant (isochoric). No work is done (P). Pressure decreases, so temperature and internal energy decrease (S).

Process 3→1: This connects high pressure to low pressure with increasing volume. Work is done by the gas (Q). It is likely the adiabatic process where internal energy changes (S).

Final Answer: (A)→(R,S), (B)→(P,S), (C)→(Q,S)