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(C) Since the two spheres are connected,the pressure $P$ in both spheres is the same.Given: Volume $V_1 = 2V_2$,Temperature $T_1 = 100 K$,$T_2 = 200 K

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$m/4$

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(C) Since the two spheres are connected,the pressure $P$ in both spheres is the same.Given: Volume $V_1 = 2V_2$,Temperature $T_1 = 100 K$,$T_2 = 200 K$.Using the ideal gas equation $PV = nRT = (m/M)RT$,where $M$ is the molar mass of the gas.For sphere $I$: $PV_1 = (m/M)RT_1$  --- $(1)$For sphere $II$: $PV_2 = (m'/M)RT_2$ --- $(2)$Dividing equation $(2)$ by equation $(1)$:$\frac{PV_2}{PV_1} = \frac{(m'/M)RT_2}{(m/M)RT_1}$$\frac{V_2}{2V_2} = \frac{m'}{m} 	imes \frac{200}{100}$$\frac{1}{2} = \frac{m'}{m} 	imes 2$$\frac{m'}{m} = \frac{1}{4}$$m' = m/4$

Two spheres are connected to each other as shown in the figure. The volume of sphere $I$ is twice the volume of sphere $II$. They contain an ideal gas at temperatures $100 K$ and $200 K$,respectively. If the mass of the gas in sphere $I$ is $m$,what is the mass of the gas in sphere $II$?

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