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

Easy

A

$\frac{T}{2}$
B

$2 T$
C

$\sqrt{2} T$
D

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

Solution

$Pv = RT = constant . (i) Also {VP}^{2} = constant . (ii) From eqn . (i) P = \frac{RT}{V} from eqn . (ii) V {(\frac{RT}{V})}^{2} = constant \frac{R^{2} T^{2}}{V} = constant or \frac{T^{2}}{V} = constant ∴ \frac{T^{2}}{V} = \frac{T^{' 2}}{2 V} or T'^{2} = 2 T^{2} ∴ T^{'} = \sqrt{2} T$

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