First slide

laws

Question

Suppose ideal gas equation follows ${VP}^{3} =$ constant. Initial temperature and volume of the gas are T and V respectively. If gas expand to 27V then its temperature will become

Moderate

A

T
B

9T
C

27T
D

$\frac{T}{9}$

Solution

${VP}^{3}$ = constant = k $\Rightarrow P = \frac{k}{V^{\frac{1}{3}}}$
Also $PV = μRT \Rightarrow P = \frac{k}{V^{\frac{1}{3}}} . V = μRT \Rightarrow V^{\frac{2}{3}} = \frac{μRT}{k}$
Hence ${(\frac{V_{1}}{V_{2}})}^{\frac{2}{3}} = \frac{T_{1}}{T_{2}} \Rightarrow {(\frac{V}{27 V})}^{\frac{2}{3}} = \frac{T}{T_{2}} \Rightarrow T_{2} = 9 T$

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