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 a container to maintain the doubled volum

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 a container to maintain the doubled volume and pressure. Assuming 1 4 th of the initial number of moles has been added in for the purpose. By what fraction the temperature must have been raised finally of initial absolute temperature?

TestHub · Accepted Answer

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

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