First slide

laws

Question

During an experiment an ideal gas is found to obey an additional law Vp² = constant. The gas is initially at temperature T and volume V. When it expands to volume 2V, the resulting temperature is [UP CPMT 2012]

Moderate

A

$\frac{T}{2}$
B

2T
C

$\sqrt{2} T$
D

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

Solution

pV = RT = constant
$\Rightarrow p = \frac{R T}{V}$
Vp² = constant
$\Rightarrow V {(\frac{R T}{V})}^{2} = constant$
$\Rightarrow \frac{R^{2} T^{2}}{V} = constant$
$\Rightarrow \frac{T^{2}}{V} = constant \Rightarrow \frac{T^{2}}{V} = \frac{T^{2}}{2 V}$
$\Rightarrow T^{' 2} = 2 T^{2} \Rightarrow T^{'} = \sqrt{2} T$

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