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(D) For an ideal gas,the equation of state is $PV = nRT = \frac{M}{M_{mol}} RT$,where $M$ is the mass of the gas.Since the pressure $P$ is constant,we

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$25$

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(D) For an ideal gas,the equation of state is $PV = nRT = \frac{M}{M_{mol}} RT$,where $M$ is the mass of the gas.Since the pressure $P$ is constant,we have $V \propto MT$,which implies $\frac{V_1}{V_2} = \frac{M_1 T_1}{M_2 T_2}$.Let the initial volume be $V_1 = 100V$,initial temperature be $T_1 = 100T$,and initial mass be $M_1 = 100M$.After the changes,the volume is reduced by $10\%$,so $V_2 = 90V$.The temperature is increased by $20\%$,so $T_2 = 120T$.Substituting these values into the proportionality equation:$\frac{100V}{90V} = \frac{100M 	imes 100T}{M_2 	imes 120T}$$\frac{10}{9} = \frac{10000M}{120M_2}$$1200M_2 = 90000M$$M_2 = \frac{90000}{1200}M = 75M$.The percentage of gas leaked is $\frac{M_1 - M_2}{M_1} 	imes 100\% = \frac{100M - 75M}{100M} 	imes 100\% = 25\%$.

$A$ 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 must leak for the pressure to remain constant?

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