How much heat is converted into work?

iceT

1) Five thousand joules of heat is put into a Carnot engine whose hot and cold reservoirs have temperatures of 500 and 250 K, respectively. How much heat is converted into work?

here's what i did.....
i know that.... QC / QH = TC / TH
W = 5000, Tc = 250, Th = 500, Qh = ?, Qc = ?

first I found Qh , which = (eCarnot = W/Qh) ----- and solve for Qh and get (Qh = W/eCarnot) ------eCarnot also equals [1-(Tc/Th)] = [1-( 250 / 500 ) ] = 0.5
so Qh = W / [1-(Tc/Th) = 5000 / 0.5 = 10000
after I got Qh I used the equation (Qc = Qh - W) to solve for Qc and this should be the answer...
Qc = Qh - W = 10000-5000 = 5000 , so Qc = 5000 ...but it still wrong



2) The pressure and volume of a gas are changed along a path ABCA in the figure. The vertical divisions on the graph represent 4.5 105 Pa, and the horizontal divisions represent 4.0 10-3 m3. Determine the work done (including algebraic sign) in each segment of the path.



a ) A to B = ? J
b ) B to C = ? J
c ) C to A = ? J

This question..i know that W= P ( Vf-Vi )
but i still cant locate the dots on the graph!!

Hootenanny

For question one the maximum efficencey of a carnot engine is given by;

[tex]1 - \frac{T_{C}}{T_{H}}[/tex]

This will give you a fraction. This in the fraction of the energy which can be used (i.e. work done). So all you need to do is multiply the input energy ([itex]Q_{H}[/itex]) by this fractional efficency.

-Hoot

Andrew Mason

The 5000 J. of heat represents Qh not W.

W = .5 Qh = 2500 J.

So only 2500 J of the 5000 is converted into work.


The work done is the area under the graph between those points.

AM