During an experiment, an ideal gas is found to obey an additional law $p V^{2}$ = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.

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Solution

$P V^{2}$ = Constant

$\Rightarrow P_{1} V_{1}^{2} = P_{2} V_{2}^{2}$

$\Rightarrow \frac{m R T_{1}}{V_{1}} \times V_{1}^{2} = \frac{m R T_{2}}{V_{2}} \times V_{2}^{2}$

$\Rightarrow T_{1} V_{1} = T_{2} V_{2}$

$\Rightarrow T V = T_{2} V_{2}$

$\Rightarrow T V = T_{2} \times$ 2 V

$\Rightarrow T_{2} = \frac{T}{2}$

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During an experiment, an ideal gas is found to obey an additional law pV2 = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.

PV2 = Constant ⇒P1V21=P2V22 ⇒mRT1V1×V21=mRT2V2×V22 ⇒T1V1=T2V2 ⇒TV=T2V2 ⇒TV=T2× 2 V ⇒T2=T2

During an experiment, an ideal gas is found to obey an additional law $p V^{2}$ = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.