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-

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-, 600 K, 400 K, 200 K, 120 K

MARKS App · Accepted Answer

Let pressure given by p i s t o n = P 0 P A + P 0 = P B or P 0 = P B - P A or P 0 = n R × 300 V / 3 – n R × 300 2 V / 3 Let the final t e m p e r a t u r e = T P B ′ = P 0 + P A ′ or P 0 = P B ′ - P A ′ or P 0 = n R T V / 5 - n R T 4 V / 5 ∴ n R T × 5 V × 3 4 = n R × 300 V × 3 × 1 2 or T × 15 4 = 300 × 3 2 or T = 4 15 × 300 × 3 2 = 120 K

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