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Gay Lussac's Law

An open vesse...

Question

An open vessel at $27^{o} C$ is heated until three fourths mass of the air in it has been expelled. Neglecting the expansion of the vessel, find the temperature to which the vessel has been heated?

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Solution

$n \propto \frac{1}{T} {n_{2} T}_{2} = {n_{1} T}_{1} ⟹ \frac{n_{2}}{n_{1}} = \frac{T_{1}}{T_{2}} ⟹ \frac{1}{4} = \frac{300 K}{T_{2}} ⟹ T_{2} = 1200 K$

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