Question

Two cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are \(m_1\) and \(m_2\), respectively. In the second cylinder, the masses of He and Ar are \(m_2\) and \(m_1\), respectively. The molar mass of Ar is \(10\) times the molar mass of He. The external pressure applied by the piston on the first cylinder needs to be \(5\) times that on the second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same temperature. Assuming He and Ar behave like ideal gases, the value of \(\left(\dfrac{m_1}{m_2}\right)\) is ____.

Hint:

For ideal gases at same temperature: \[ V \propto \frac{n}{P} \] Always:
• first calculate total moles
• then apply ideal gas proportionality
• carefully substitute pressure ratios Also remember: \[ n = \frac{m}{M} \] where \(m\) is mass and \(M\) is molar mass.

Answer 1