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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

Verified by Experts

(i)
`T = (PV)/(nR) = (1 xx 20)/(2 xx 0.082) = 121.95` K
(ii) Total work (W) `=W_(1) + W_(2) + W_(3)`
`= -1 xx 20 + 2.303 xx 2 xx 0.082 xx 121.95 log2`
`=-20 + 13.86 = -6.13` L atm.
Since the system has returned to its initial state, i.e. the process is cyclic. So, `DeltaU=0`
`DeltaU = q+W=0`
`q=-W = 6.13 L atm = 620.7` J
In a cyclic process heat absorbed is completely converted into work.
Entropy is a state function and since the system has returned to its initial state so `DeltaS=0`. Similarly, `DeltaH=0` and `DeltaU=0` for the same reason, i.e. U and H are also state functions having definite values in a given state of a system.
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