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One mole of an ideal gas (C(v) = 3/2R) i...

One mole of an ideal gas `(C_(v) = 3/2R)` is heated at constant pressure of 1 atmosphere from `25^(@)` C to `100^(@)` C. Calculate `DeltaE` and `DeltaH`.

Text Solution

Verified by Experts

As `(C_(P) - C_(v)) = R rArr C_(p)=C_(v) + R`
`rArr C_(p) = 3/2 R + R= 5/2 R`
Heat given at constant pressure.
`(DeltaH) = nC_(p)DeltaT = 1 x 5/2 R xx (373 - 298)`
`rArr (DeltaH) = 1 xx 5/2 xx 1.987 xx 75 = 372.56` cal
Work done in the process = `-PDeltaV`
`=-P(V_(2)-V_(1))`
`=-P((nRT_(2))/P -(nRT_(1))/P)` (As PV = nRT)
`=-nR(T_(2)-T_(1))`
`=-1 xx 1.987 xx (373 - 298)`
`=-149.05` cal.
From first law of thermodynamics.
`DeltaE = q+W`
`=372.56 - 149.05`
=223.51 cal.
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