Question

A gas is present in a cylinder fitted with movable piston. Above and below of 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. 600 K
• B. 400 K
• C. 200 K
• D. 120 K

Answer 1

Answer: (D)

120 K

Answer 2

Let press given by piston = P₀

P_A + P₀ = P_B

or P₀ = P_B – P_A

or P₀ = $\frac{nR \times 300}{V/3}$ – $\frac{nR \times 300}{2V/3}$

Let the final temperature = T

P¢_B = P₀ + P¢_A

or P₀ = P¢_B – P¢_A

or P₀ = $\frac{nRT}{V/5}$ – $\frac{nRT}{4V/5}$

\ $\frac{nRT \times 5}{V}$ × $\frac{3}{4}$ = $\frac{nR \times 300}{V}$ × 3 × $\frac{1}{2}$

or T × $\frac{15}{4}$ = 300 × $\frac{3}{2}$

or T = $\frac{4}{15}$ × 300 × $\frac{3}{2}$ = 120 K