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 $300K$ . At what temperature will the volume above be four times the volume below-

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

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 $P_0=\frac{nR\times 300}{V/3}-\frac{nR\times 300}{2V/3}$
Let the final $temperature=T$




$P_B^{\prime }=P_0+P_A^{\prime }$
or $P_0=P_B^{\prime }-P_A^{\prime }$
or $P_0=\frac{nRT}{V/5}-\frac{nRT}{4V/5}$
$\therefore \frac{nRT\times 5}{V}\times \frac{3}{4}=\frac{nR\times 300}{V}\times 3\times \frac{1}{2}$
or $T\times \frac{15}{4}=300\times \frac{3}{2}$
or $T=\frac{4}{15}\times 300\times \frac{3}{2}=120K$