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(C) For an ideal gas,the ideal gas equation is given by $PV = \frac{m}{M}RT$,where $P$ is pressure,$V$ is volume,$m$ is mass,$M$ is molar mass,$R$ is

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$\frac{m}{4}$

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(C) For an ideal gas,the ideal gas equation is given by $PV = \frac{m}{M}RT$,where $P$ is pressure,$V$ is volume,$m$ is mass,$M$ is molar mass,$R$ is the universal gas constant,and $T$ is temperature.Since the flasks are connected,the pressure $P$ is the same in both flasks. Also,the gas is the same,so $M$ is constant.Thus,$V \propto \frac{mT}{P} \Rightarrow V \propto mT$.We can write the ratio as: $\frac{V_1}{V_2} = \frac{m_1 T_1}{m_2 T_2}$.Given $V_1 = 2V_2$,$T_1 = 100\, K$,$T_2 = 200\, K$,and $m_1 = m$.Substituting these values: $\frac{2V_2}{V_2} = \frac{m 	imes 100}{m_2 	imes 200}$.$2 = \frac{m}{2m_2}$.$4m_2 = m \Rightarrow m_2 = \frac{m}{4}$.

The figure shows two flasks connected to each other. The volume of flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperatures $100\, K$ and $200\, K$ respectively. If the mass of the gas in flask $1$ is $m$,what is the mass of the gas in flask $2$?

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