Question

One mole of an ideal monatomic gas undergoes the process `p=alphaT^(1//2)` , whwre a is a constant. The work done by the gas if its temperature increases by `50K` is `(50R)/(x)`. Find the value of x.

Answer 1

Correct Answer - B
`P=alphaT^(1//2)` ……..`(i)`
where `alpha` is constant `n=1` mol, monaatomic
`W=intPdV=int(alphaT^(1//2))dV`
From equation `(i)` `T=(alphaT^(1//2)V)/(nR)impliesT(1//2)=(alphaV)/(nR)`
Differentiating both sides,
`(1)/(2sqrtT)dT=(alphadV)/(nR)impliesdV=(nR)/(alpha2sqrtT)dT`
`W=intalphaT^(1//2)(nR)/(2T^(1//2))dT`
`=(nalphaR)/(2)int_(T_(1))^(T_(2))dT=(R)/(2)xx50=25RJ`