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(D) The ideal gas equation is $PV = nRT$,where $n$ is the number of moles.Taking the natural logarithm on both sides: $\ln(PV) = \ln(nRT) = \ln(n) + \

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$30$

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(D) The ideal gas equation is $PV = nRT$,where $n$ is the number of moles.Taking the natural logarithm on both sides: $\ln(PV) = \ln(nRT) = \ln(n) + \ln(R) + \ln(T)$.Differentiating the equation,we get: $\frac{\Delta P}{P} + \frac{\Delta V}{V} = \frac{\Delta n}{n} + \frac{\Delta T}{T}$.Since the gas is in a cylinder and we are considering the leakage at constant pressure (assuming the external pressure remains constant),$\Delta P = 0$.Given: $\frac{\Delta V}{V} 	imes 100 = -10\%$ and $\frac{\Delta T}{T} 	imes 100 = +20\%$.Substituting these values into the equation: $0 + (-10) = \frac{\Delta n}{n} 	imes 100 + 20$.Rearranging for the percentage change in moles: $\frac{\Delta n}{n} 	imes 100 = -10 - 20 = -30\%$.The negative sign indicates that $30\%$ of the gas has leaked out.

$A$ gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and its volume is reduced by $10\%$. How much percentage of the gas will leak out?

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