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 $\frac{1}{4}th$ of initial number of moles has been added in for the purpose. By what fraction the temperature must has been raised finally of initial absolute temperature ?

• A. 4 times
• B. $\frac{16}{5}$ times
• C. $\frac{4}{5}$times
• D. $\frac{1}{5}$ times

Answer 1

Answer: (B)

$\frac{16}{5}$ times

Answer 2

I initially : Pressure P volume V temp T moles x.

II on 2P 2V then temperature heating becomes 4T After decreasing temperature :

III Pressure volume Temperature moles 2P 2V T' (assume) n +$\frac{n}{4}$= $\frac{5n}{4}$ for II case ideal

gas equation 2P × 2V = n × R × 4T

III case

2P × 2V = $\frac{5n}{4}$ × R × T' ̃ T ' = $\frac{16}{5}$ T