First slide

Different type of processes

Question

An ideal gas is found to obey the relation ${PV}^{\frac{3}{2}}$ = constant during an adiabatic process. If such a gas initially at a temperature T is compressed to half of initial volume, then its final temperature will be

Moderate

A

2T
B

$\sqrt{2 T}$
C

$2 \sqrt{2} T$
D

4T

Solution

${PV}^{\frac{3}{2}} = constant \Rightarrow γ = \frac{3}{2} so from T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1} We have T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{\frac{1}{2}} = T {(\frac{V}{V / 2})}^{\frac{1}{2}} = \sqrt{2} T$

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