Question #42596

A cylindrical spacecraft of length $L$ and cross-sectional area $A$ accelerates uniformly at $a$ along its longitudinal axis in deep space. It contains an equimolar ideal gas mixture of Gas 1 (molecular mass $m_1$) and Gas 2 (molecular mass $m_2 = 4m_1$) maintained at a constant temperature $T$. A microscopic leak develops at the flat rear wall of the spacecraft (the trailing end). Given that the acceleration satisfies $a = \frac{kT}{m_1 L} \ln 2$, where $k$ is the Boltzmann constant, what is the initial ratio of the mass escape rate of Gas 2 to Gas 1, $\frac{dM_2/dt}{dM_1/dt}$?