ThermodynamicsHard
Question
An adiabatic cylinder fitted with an adiabatic piston at the right end of cylinder is divided into two equal halves with a monoatomic gas on left side and diatomic gas on right side using an impermeable movable adiabatic wall. If the piston is pushed slowly to compress the diatomic gas to (¾)th of its original volume. The ratio of new volume of monoatomic gas to its initial volume would be
Options
A.$\left( \frac{4}{3} \right)^{\frac{25}{21}}$
B.$\left( \frac{7}{5} \right)^{\frac{3}{4}}$
C.$\left( \frac{3}{4} \right)^{\frac{21}{25}}$
D.$\frac{3}{4}$
Solution
Monoatomic: $P_{1}.V_{0}^{5/3} = P_{2}.V_{1}^{5/2}$
Diatomic: $P_{1}.V_{0}^{7/5} = P_{2}.\left( \frac{3}{4}V_{0} \right)^{7/5}$
$\therefore\frac{V_{1}}{V_{0}} = \left( \frac{3}{4} \right)^{\frac{21}{25}}$
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