Consider two containers A and B containing id | vedclass

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Question

When the compression is isothermal for gas in $A$

$P_{2} V_{2}=P_{1} V_{1}$

$P_{2}=P_{1} \frac{V_{1}}{V_{2}}=P_{1} \frac{V_{1}}{V_{1} / 2}=2 P_{

Vedclass · Accepted Answer

$2^{\gamma-1}$

Vedclass · Answer

When the compression is isothermal for gas in $A$

$P_{2} V_{2}=P_{1} V_{1}$

$P_{2}=P_{1} \frac{V_{1}}{V_{2}}=P_{1} \frac{V_{1}}{V_{1} / 2}=2 P_{1}$

For gas in $\mathrm{B}$, when compression is adiabatic,

$P_{2}^{\prime} V_{2}^{\prime}=P_{1} V_{1}^{\gamma}$

$P_{2}^{\prime}=P_{1}\left(\frac{V_{1}}{V_{2}^{\prime}}ight)^{\gamma}=P_{1}\left(\frac{V_{1}}{V_{1} / 2}ight)^{\gamma}=2^{\gamma} P_{1}$

$	herefore \frac{P_{2}^{\prime}}{P_{2}}=\frac{2^{\gamma} P_{1}}{2 P_{1}}=2^{\gamma-1}$

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