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JEE Main 20249 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Morning Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2024 · 9 April · Morning Shift · Physics · Thermodynamics

The volume of an ideal gas (γ=1.5) is changed adiabatically from 5...

The volume of an ideal gas (γ=1.5)(\gamma=1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

Options

  1. A1625\frac{16}{25}
  2. B45\frac{4}{5}
  3. C855\frac{8}{5 \sqrt{5}}
  4. D25\frac{2}{\sqrt{5}}

Correct answer

C. 855\frac{8}{5 \sqrt{5}}

Step-by-step solution

For Adiabatic process PiVi=PfVfγPi(5)1.5=Pf(4)1.5PiPf=(45)32=45⋅(45)12⇒855\begin{aligned} & P_i V_i=P_f V_f^\gamma \\ & P_i(5)^{1.5}=P_f(4)^{1.5} \\ & \frac{P_i}{P_f}=\left(\frac{4}{5}\right)^{\frac{3}{2}}=\frac{4}{5} \cdot\left(\frac{4}{5}\right)^{\frac{1}{2}} \Rightarrow \frac{8}{5 \sqrt{5}}\end{aligned}
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