Vertical closed cylinder| KTG & THERMODYNAMICS|JEE MAIN 2019

JEE MAIN 2019

12-01-2019 S2

Question

A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $\mathrm{I}_1$, and that below the piston is $\mathrm{I}_2$, such that $\mathrm{I}_1>\mathrm{I}_2$. Each part of the cylinder contains n moles of an ideal gas at equal temperature T . If the piston is stationary, its mass, m will be given by: ( R is universal gas constant and g is the acceleration due to gravity)

Select the correct option:

$\frac{\mathrm{nRT}}{\mathrm{g}}\left[\frac{\mathrm{I}_1-\mathrm{I}_2}{\mathrm{I}_1 \mathrm{I}_2}\right]$

$\frac{\mathrm{nRT}}{\mathrm{g}}\left[\frac{1}{\mathrm{I}_2}+\frac{1}{\mathrm{I}_1}\right]$

$\frac{R T}{g}\left[\frac{2 I_1+I_2}{I_1 I_2}\right]$

$\frac{\mathrm{RT}}{\mathrm{ng}}\left[\frac{\mathrm{I}_1+3 \mathrm{I}_2}{\mathrm{I}_1 \mathrm{I}_2}\right]$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution