Question

A closed vertical cylinder is divided into two parts by a frictionless piston, each part contains 1 mole of air. At ${27}^{\circ }C$ the volume of the upper part is 4 times than that of the lower part. Calculate the temperature (T) when volume of the upper part will be three times that of the lower part. (write answer to nearest integer function)

Answer 1

The Volume and Temperature are as shown in the above figure.

Initially,
$P_{lower}=P_{upper}+P_{piston}$

$5\times \frac{R\times 300}{V}=5\times \frac{R\times 300}{4V}+P_{piston}$
$P_{piston}=\left(\frac{5R\times 300}{V}\right)\times \frac{3}{4}$............(1)

Finally,
$P_{lower}=P_{upper}+P_{piston}$

$\frac{4RT}{V}=\frac{4RT}{3V}+P_{pistion}$

$\frac{8RT}{3V}=P_{piston}$ ...(2)

From equation (1) & and (2)

$\frac{15}{4}\times \frac{R\times 300}{V}=\frac{8RT}{3V}\Rightarrow T=421.9K$

Answer is $422$.