First slide

laws

Question

During an experiment an ideal gas is found to obey an additional law VP² = constant. The gas is initially at a temperature 'T' and volume
'V'. When it expands to a volume 2V, the temperature becomes

Moderate

A

T
B

2T
C

$\sqrt{2} T$
D

$\frac{T}{\sqrt{2}}$

Solution

$PV \propto T, \frac{P_{1}}{P_{2}} \times \frac{V_{1}}{V_{2}} = \frac{T_{1}}{T_{2}}$
According to given data P²V= constant
$\Rightarrow \frac{P_{1}}{P_{2}} = {(\frac{V_{2}}{V_{1}})}^{\frac{1}{2}} \Rightarrow \frac{T_{1}}{T_{2}} = {(\frac{V_{2}}{V_{1}})}^{\frac{1}{2}} (\frac{V_{1}}{V_{2}})$

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