\( 0.5 \) mole of an ideal gas is kept inside an adiabatic cylinder of length L and cross-sectio...

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\( 0.5 \) mole of an ideal gas is kept inside an adiabatic cylinder of length L and cross-sectional area A closed by massless adiabatic piston. The cylinder is attached with a con-
P ducting rod of length \( L \) , cross-sectional area \( \frac{1}{900} \mathrm{~m}^{2} \)
D. and thermal conductivity \( 415.5 \mathrm{~W} / \mathrm{m}-\mathrm{K} \), whose other end is maintained at \( 0^{\circ} \mathrm{C} \). The piston is moved such that the temperature of the gas remains constant at \( 27^{\circ} \mathrm{C} \). Find the velocity (in \( \mathrm{mm} / \mathrm{sec} \) ) of piston when it is at height \( \mathrm{L} / 2 \) from the bottom of cylinder. Rod is well lagged and has negligible heat capacity. \( \mathrm{R}=8.31 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \).
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