Thermodynamics

JEE Main level, single correct, medium

96 of 190

Question 96 of 190

The initial pressure and volume of an ideal gas areP0{P}_{0} and V0{V}_{0}. The final pressure of the gas when the gas is suddenly compressed to volumeV04\dfrac{{V}_{0}}{4} will be:
(Given γ\gamma= ratio of specific heats at constant pressure and at constant volume.)

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Answer: (A) P0(4)γ{P}_{0}(4{)}^{\gamma }

As the gas is suddenly compressed the process is adiabatic.
So, PVγ=constantP{V}^{\gamma }=constant
⇒P0V0γ=P⋅(V04)γ\Rightarrow {P}_{0}{V}_{0}^{\gamma }=P\cdot {\left(\dfrac{{V}_{0}}{4}\right)}^{\gamma }
⇒P=4γ⋅P0\Rightarrow P={4}^{\gamma }\cdot {P}_{0}

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