Physics Circle home Student Login

Home›Chapters›Thermodynamics PYQs›Heat Engines, Refrigerators & Second Law›Question 18

MHT CET 2024 (3 May, Shift 1) · Heat Engines, Refrigerators & Second Law

Heat Engines, Refrigerators & Second Law question from MHT CET 2024 (3 May, Shift 1)

Q18MHT CET 2024 · 3 MAY · SHIFT 1Difficult

Heat Engines, Refrigerators & Second Law

A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V, the efficiency of the engine is

Show answer and solution

Answer: (c)

  1. Adiabatic: TVγ−1=TV^{\gamma - 1} = constant, with γ=75\gamma = \frac{7}{5} for a diatomic gas.
  2. T2T1=(V32V)2/5=(12)2=14\frac{T_2}{T_1} = \left(\frac{V}{32V}\right)^{2/5} = \left(\frac{1}{2}\right)^{2} = \frac{1}{4}
  3. η=1−T2T1=1−14=0.75\eta = 1 - \frac{T_2}{T_1} = 1 - \frac{1}{4} = 0.75
  4. So the answer is (c) 0.75.
Report a mistake

More questions on Heat Engines, Refrigerators & Second Law