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  4. By increasing temperature of a gas by 6° C its pressure increases by 0.4 %, at constant volume. Then initial temperature of gas is

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Q. By increasing temperature of a gas by $6^{\circ} C$ its pressure increases by $0.4 \%$, at constant volume. Then initial temperature of gas is

Kinetic Theory

Solution:

$\frac{P_{2}}{P_{1}}=\frac{T_{2}}{T_{1}}$
$ T_{1}=T$
$T_{2}=T+6$
$\frac{P_{2}}{P_{1}}-1=\frac{T_{2}}{T_{1}}-1$
$\frac{P_{2}-P_{1}}{P_{1}} \times 100=\left(\frac{T+6}{T}-1\right) 100$
$0.4=\frac{600}{T} \Rightarrow T=1500\, K$