First slide

Different type of processes

Question

An ideal gas at a pressures of 1 atmosphere and temperature of 27⁰C is compressed adiabatically until its pressure becomes 8 times the initial pressure, then the final temperature is $(γ = 3 / 2)$ :

Moderate

A

$627^{\circ} C$
B

$527^{\circ} C$
C

$427^{\circ} C$
D

$327^{\circ} C$

Solution

Using relation
$= \frac{T_{2}}{T_{1}} = {(\frac{P_{2}}{P_{1}})}^{\frac{γ - 1}{γ}} = (8)^{\frac{3 / 2 - 1}{3 / 2}} = 2$
$\Rightarrow T_{2} = 2 T_{1}$
$\Rightarrow T_{2} = 2 (273 + 27) = 600 K = 327^{0} C$

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