Question

A gas expands adiabatically at constant pressure such that its temperature `Tprop(1)/(sqrt(V))` , the value of `C_(P)//C_(V)` of gas is
A. `1.30`
B. `1.50`
C. `1.67`
D. `2.00`

Answer 1

Correct Answer - B
For adiabatic expansion , we have the formula `pV^(gamma)` = Constant ... (i)
Gas equation is ,
`pV=RTrArrp=(RT)/(V)` …(ii)
From Eqs . (i) and (ii) , we obtain
`((RT)/(V))V^(gamma)` = constant
`rArr" " TV^(gamma-1)` = constant ...(iii)
`"But " Tprop(1)/(sqrtV)` (given) `
"as " TV^(1//2)` = constant ...(iv)
THus , using Eqs. (iii)and (iv) together, we get
`gamma-1=(1)/(2)`
`"or " gamma=(3)/(2)=1.5rArr(C_(p))/(C_(v))=1.5`