A gas is heated in such a way that its pressure and volume both becomes double. Then by decreasing temperature, some of the molecules of air has been added in container to maintain the doubled volume and pressure. Assuming 1 4 t h of initial number of moles has been added in for the purpose. The fraction by which the temperature must have been raised finally of initial absolute temperature?

Question

A gas is heated in such a way that its pressure and volume both becomes double. Then by decreasing temperature, some of the molecules of air has been added in container to maintain the doubled volume and pressure. Assuming 1 4 t h of initial number of moles has been added in for the purpose. The fraction by which the temperature must have been raised finally of initial absolute temperature?, 4 t i m e s, 16 5 t i m e s, 4 5 t i m e s, 1 5 t i m e s

MARKS App · Accepted Answer

I initially : Pressure P volume V temp T moles x . II on 2 P, 2 V then temperature heating becomes 4 T After decreasing temperature : 2P × 2V = n × R × 4T III Pressure volume Temperature moles 2 P, 2 V, T ′ (assume) n + n 4 = 5 n 4 I I I case 2 P × 2 V = 5 n 4 × R × T ′ ⇒ T ′ = 16 5 T

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