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MHT CET 2023 (14 May, Shift 2) · Thermodynamic Processes

Thermodynamic Processes question from MHT CET 2023 (14 May, Shift 2)

Q147MHT CET 2023 · 14 MAY · SHIFT 2Medium

Thermodynamic Processes

The pressure and density of a diatomic gas (γ=75)\left(\gamma = \frac{7}{5}\right) changes adiabatically from (P,ρ)(P, \rho) to (P′,ρ′)(P', \rho'). If ρ′ρ=32\frac{\rho'}{\rho} = 32 then P′P\frac{P'}{P} should be

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Answer: (b)

  1. ρ∝1V\rho \propto \frac{1}{V}, so PVγ=constPV^\gamma = \text{const} gives P∝ργP \propto \rho^\gamma.
  2. P′P=327/5=27=128\frac{P'}{P} = 32^{7/5} = 2^7 = 128
  3. So the answer is (b) 128.
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