First slide

laws

Question

At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its volume is [Manipal 2015]

Moderate

A

1/T
B

1/T²
C

T
D

T²

Solution

According to the ideal gas law,
$\Rightarrow p V = R T \Rightarrow V = (\frac{R}{p}) T$
$\Rightarrow V \propto T \Rightarrow \frac{V_{1}}{V_{2}} = \frac{T_{1}}{T_{2}}$
$\Rightarrow \frac{V_{2}}{V_{1}} - 1 = \frac{T_{2}}{T_{1}} - 1$
$\Rightarrow \frac{V_{2} - V_{1}}{V_{1}} = \frac{T_{2} - T_{1}}{T_{1}}$
$\Rightarrow \frac{V_{2} - V_{1}}{V_{1}} = \frac{1}{T_{1}} = \frac{1}{T}$

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