(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

thermal efficiency = Wout/QH

(thermal efficiency)Carnot = 1 - TC/TH

3. 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 thats the wrong answer!

I don't know what's wrong. Help!

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# Homework Help: Heat engine.

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