' $\mathrm{V}$ ' cc volume of a gas having $\mathrm{Y}=\frac{5}{2}$ is suddenly compressed to…

' $\mathrm{V}$ ' cc volume of a gas having $\mathrm{Y}=\frac{5}{2}$ is suddenly compressed to $\left(\frac{V}{4}\right)$ c.c. The initial pressure of the gas is P. The final pressure of the gas will be
  1. $\frac{\mathrm{P}}{32}$
  2. $16 \mathrm{P}$
  3. $\frac{\mathrm{P}}{16}$
  4. $32 \mathrm{P}$

Solution

Here, $\mathrm{V}_1=\mathrm{V}$ cc, $\mathrm{V}_2=\frac{\mathrm{v}}{4} \mathrm{cc}, \mathrm{Y}=\frac{5}{2}, \mathrm{P}_1=\mathrm{P}$ for adiabatic change, $\begin{aligned} & \mathrm{P}_2 \mathrm{~V}_2=\mathrm{P}_1 \mathrm{~V}_1^{\mathrm{Y}} \\ & \therefore \mathrm{P}_1=\mathrm{P}\left\{\frac{\mathrm{V}}{\left(\frac{\mathrm{V}}{4}\right)}\right\}^Y \\ & \mathrm{P}_2=\mathrm{P}(4)^{5 / 2}=\mathrm{P}\left(2^5\right)=32 \mathrm{P}\end{aligned}$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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