There is a heat-insulated vessel standing on a table with an ideal monoatomic gas under a freely moving piston, in equilibrium (Fig. a). On the upper side of the piston is vacuum. The piston is fixed, the vessel is tilted at an angle $α$ such that $\cos α = \frac{3}{8}$ and the piston is released again (Fig. b). Find the ratio of final volume of gas in steady state to initial volume of gas

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answer is 2.

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Detailed Solution

Let ν 𝜈 - number of moles of gas, m be mass of - piston m,T1,V1,T2,V2 - initial and final temperatures and volumes of gas, and the area of piston be S.. Let's write down the law of conservation of energy
$ν \frac{3}{2} R T_{1} = ν \frac{3}{2} R T_{2} + m g \frac{V_{2} - V_{1}}{S} \cos α$
For the initial and final states of the gas $\frac{m g}{S} V_{1} = ν R T_{1}, \frac{m g \cos α}{S} V_{2} = ν R T_{2}$