Thermodynamics

JEE Main level, single correct, medium

84 of 190

Question 84 of 190

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:

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Answer: (C) 855\frac{8}{5 \sqrt{5}}

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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