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An ideal diatomic gas (gamma=7/5) underg...

An ideal diatomic gas `(gamma=7/5)` undergoes a process in which its internal energy relates to the volume as `U=alphasqrtV`, where `alpha` is a constant.
(a) Find the work performed by the gas to increase its internal energy by 100J.
(b) Find the molar specific heat of the gas.

Text Solution

Verified by Experts

The correct Answer is:
`(i)80J , 180J` (ii) 4.5 R`
For the process `U = asqrt(V) implies nC_(V)T = n(5)/(2)RT = asqrt(V)`
`implies nRT = PV = (2)/(5)asqrt(V) implies P = (2)/(5)(a)/(sqrt(V))`
`implies W = intPdV = (4)/(5)a(sqrt(V))_(v_(t))^(v_(f))`
`because DeltaU = a(sqrt(V))_(v_(t))^(v_(f))= 100`
`therefore W = (4)/(5)DeltaU = 80J`
(i) `W=80J`
`Q = DeltaU + W = 100J + 80J = 180J`
(ii) `C =(DeltaQ)/(nDeltaT) = (DeltaU +W)/(nDeltaT) = (DeltaU + (4)/(5)DeltaU)/(nDeltaT)`
=`(9)/(5)((DeltaU)/(nDeltaT))= (9)/(5)xx (5)/(2)R = (9)/(2)R0`
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