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An ideal gas at a pressures of 1 atmosphere and temperature of $27^{°} C$ is compressed adiabatically until its pressure becomes 8 times the initial pressure, then the final temperature is $(γ = 3 / 2)$

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$627^{°} c$

$427^{°} c$

$327^{°} c$

$527^{°} c$

answer is D.

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Detailed Solution

In adapter processes pressure and temperature are related as

$P T^{\frac{γ}{γ - 1}} = co n s t$

${(\frac{P_{1}}{P_{2}})}^{1 - γ} = {(\frac{T_{2}}{T_{1}})}^{5} {\Rightarrow (\frac{1}{8})}^{1 - 1.5} = {(\frac{T_{2}}{300})}^{1.5}$

$T_{2} = 300 \times 8^{\frac{0 .5}{1 .5}} = 300 (2) = 600 K = 327^{0} C$

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