First slide

laws

Question

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

Moderate

A

T
B

2T
C

$T \sqrt{2}$
D

$\frac{T}{2}$

Solution

PV = RT (ideal gas equation)---------(i)
$V^{2} P = C (additional law)$ -----------(ii)
Dividing V = $\frac{C}{RT} \Rightarrow V \propto \frac{1}{T}$
or $T = \frac{1}{V} (combined law)$
When volume (V) is doubled, temperature is halved
i.e., $T^{'} = \frac{T}{2}$

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