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

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Solution

The law obeyed by the ideal gas is: $P V^{2} =$ constant

The law can be simplified as:
$\Rightarrow P_{1} V_{1}^{2} = P_{2} V_{2}^{2}$

Since the gas is ideal gas, so it can be simplified using ideal gas:

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

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

$\Rightarrow T V = T_{1} \times 2 V$

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

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

The law obeyed by the ideal gas is: PV2= constantThe law can be simplified as:⇒P1V21=P2V22Since the gas is ideal gas, so it can be simplified using ideal gas:⇒nRT1V1×V21=nRT2V2×V22⇒T1V1=T2V2⇒TV=T1×2V⇒T2=T2

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