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Homework Statement
A heat engine using 5.00 g of helium gas is initially at STP. The gas goes through the following closed cycle:
- Isothermal compression until the volume is halved.
- Isobaric expansion until the volume is restored to its initial value.
- Isochoric cooling until the pressure is restored to its initial value.
a)How much work does this engine do per cycle?
b)What is its thermal efficiency?
Homework Equations
thermal efficiency = Wout/QH
(thermal efficiency)Carnot = 1 - TC/TH
The Attempt at a Solution
for part a) I got:
isothermal work = nRTln(V at 2/V at 1) = -1967 J
isobaric work = p(V at 3 - V at 2) = 2836 J
isochoric work = 0
total work done in one cycle = -1967 + 2836 = 869 J
for pat b) i got:
from 1 to 2:
Q = -W = 1967 J
from 2 to 3:
Q = nC_p(deltaT), C_p for a monatomic gas is (5/2)R, this comes from the equipartition theorem
Q = (1.25)(5R/2)(273K) = 7094 J
from 3 to 1:
Q must be negative since there is a work output so therefore Q in this process is irrelevant since we only need the Q that is added to the system
efficiency = (total work done in one cycle)/(heat added in one cycle)
efficiency = (869 J)/(7094 J + 1967 J) = 0.096=9.6% But apparently that's the wrong answer!
I don't know what's wrong. Help!
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