Question

A gas is present in a cylinder fitted with movable piston. Above and below the piston there is equal number of moles of gas. The volume above is two times the volume below at a temperature of $ \, 300 \, K$ . At what temperature will the volume above be four times the volume below-

• A. $600 \, K$
• B. $400 \, K$
• C. $200 \, K$
• D. $120 \, K$

Answer 1

Answer: (D)

Let pressure given by $piston=P_{0}$
$P_{A}+P_{0}=P_{B}$
or $P_{0}=P_{B}- \, P_{A}$
or $P_{0}=\frac{n R \, \times \, 300}{V / 3} \, - \, \frac{n R \, \times \, 300}{2 V / 3}$
Let the final $temperature=T$




$P_{B}^{′}=P_{0}+P_{A}^{′}$
or $P_{0}=P_{B}^{′}-P_{A}^{′}$
or $P_{0}=\frac{n R T}{V / 5}- \, \frac{n R T}{4 V / 5}$
$\therefore \frac{n R T \times 5}{V} \, \times \, \frac{3}{4}=\frac{n R \times 300}{V} \, \times \, 3 \, \times \, \frac{1}{2}$
or $T \, \times \, \frac{15}{4}=300 \, \times \, \frac{3}{2}$
or $T=\frac{4}{15} \, \times \, 300 \, \times \, \frac{3}{2}=120 \, K$