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Two moles of a perfect gas undergo the f...

Two moles of a perfect gas undergo the following processes:
a. A reversible isobaric expansion from `(1.0 atm, 20.0L)` to `(1.0 atm, 40.0L)`.
b. A reversible isochroic change of state from `(1.0 atm, 40.0L)` to `(0.5 atm, 40.0 L)`
c. A reversible isothermal expansion from `(0.5 atm, 40.0 L) to(1.0 atm, 20.0 L)`.
i. Sketch with lables each of the processes on the same `P -V` diagram.
ii. Calculate the total work `(w)` and the total heat change `(q)` involved in the above process.
iii. What will be the values of `DeltaH` for the overall process?

Text Solution

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(ii)Total work `(w) = w_(1)+w_(2)+w_(3) =- P DeltaV+ 0 + 2.303 nRT log .(V_(1))/(V_(2))`
`= -1 xx 20+2.303 xx 2 xx 0.082 xx 121.95 log 2 (T =(PV)/(nR) = ( 1 xx 20)/( 2 xx 0.082) = 121.95 K) `
`= -20 + 13.86 = - 6.13L atm=-6.13 xx 101.3 J = - 621.0 J `
(In a cyclic process,heat abosorbed is completely converted into work)
(iii) As U, H and S are state functions and the system has returned to its original state, `DeltaU =0, DeltaH=0,` and`Delta S=0`.
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