The initial pressure and volume of an ideal gas are \(P_0\) and \(V_0\). The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{ V _0}{4}\) will be (Given \(\gamma=\) ratio of specific heats at constant pressure and at constant volume)

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Answer & Solution

Correct Answer

(B) \(P _0(4)^\gamma\)

Step-by-step Solution

Detailed explanation

As gas is suddenly compressed, the processes is adiabatic.

Equation of gas for adiabatic process is

\(PV ^\gamma=\text { constant. }\)

\(\Rightarrow P _1 V _1^\gamma= P _2 V _2^\gamma\)

\(\Rightarrow P _0 V _0^\gamma= P _2\left(\frac{ V _0}{4}\right)^\gamma\)

\(\Rightarrow P _2= P _0(4)^\gamma\)

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