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(A) For a gas in a closed vessel of constant volume,Gay-Lussac's Law states that $P \propto T$,where $P$ is the pressure and $T$ is the absolute tempe

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$100 \ K$

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(A) For a gas in a closed vessel of constant volume,Gay-Lussac's Law states that $P \propto T$,where $P$ is the pressure and $T$ is the absolute temperature in Kelvin.Taking the derivative,we have $\frac{dP}{P} = \frac{dT}{T}$.Given that the pressure increases by $1 \%$,we have $\frac{dP}{P} = 0.01$.Given that the temperature increases by $dT = 1 \ K$ (since a change of $1^{\circ} C$ is equivalent to a change of $1 \ K$).Substituting these values into the equation: $0.01 = \frac{1}{T}$.Therefore,$T = \frac{1}{0.01} = 100 \ K$.

The temperature of a gas contained in a closed vessel of constant volume increases by $1^{\circ} C$ when the pressure of the gas is increased by $1 \%$. The initial temperature of the gas is

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