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NEET 2014
Exam
NEET
Year
2014
Subject
Physics
Chapter
Thermodynamics

NEET 2014 · Physics · Thermodynamics

A monoatomic gas at a pressure P, having a volume V expands...

A monoatomic gas at a pressure P,P, having a volume VV expands isothermally to a volume 2V2V and then adiabatically to a volume 16V.16V . The final pressure of the gas is: (take γ=5/3\gamma = 5 / 3)

Options

  1. A64P64P
  2. B32P32P
  3. CP/64P / 64
  4. D16P16P

Correct answer

C. P/64P / 64

Step-by-step solution

Isothermally PV=P12VPV = {P}_{1}2V
P1=P2{P}_{1} = \dfrac{P}{2}
Adiabatically
P2(2V)γ=Pf(16V)γ\dfrac{P}{2}{\left(2V\right)}^{\gamma} = {P}_{f}{\left(16V\right)}^{\gamma}
Pf=P2(123)53{P}_{f} = \dfrac{P}{2}{\left(\dfrac{1}{{2}^{3}}\right)}^{\dfrac{5}{3}}
Pf=P2(123)53=P(2)(2)5{P}_{f} = \dfrac{P}{2}{\left(\dfrac{1}{{2}^{3}}\right)}^{\dfrac{5}{3}} = \dfrac{P}{\left(2\right){\left(2\right)}^{5}}
Pf=p64{P}_{f} = \dfrac{p}{64}
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