Question

A heat engine produces 8200 J of heat while performing 3200 of useful work. What is the efficiency of this engine? (I'm doing something wrong.)

Answer 1

Q = 8200 J (i'm not sure if this is Q(h) or Q(c). I think it's Q(h) ?
W = 3200 J
e = W/Q(h)
e = 3200/8200
39%
my answer's wrong. (it should be 28%)

Answer 2

i just don't really understand why the 8200 J would be the heat wasted.

Answer 3

@Kainui help again? sowwy.

Answer 4

So from this carnot engine (the circle) that it takes in energy with heat and then the energy leaves as both work and heat at a colder temperature

Qh=Qc+W

Since efficiency is how good you are at getting work out of the work you put in, E=W/Qh.

However since we're not given the value of the heat we put in, we're told the heat that came out, we can just substitute in the first equation.

Answer 5

I hope that makes sense, I feel like my english just flopped on its face right there. I can answer any questions about the carnot cycle or whatever you may need.

Answer 6

Another substitution in a carnot engine is realizing that the ratio of heats to temperatuers is equal.

\[\frac{ q_h }{ q_c }=\frac{ T_h }{ T_c }\]

Answer 7

So for example you can find the efficiency entirely based off the temperatures:

\[E=\frac{ w }{ q_h }=\frac{ q_h-q_c }{ q_h }=1-\frac{ q_c }{ q_f }=1-\frac{ T_c }{ T_h}\]

Answer 8

Luckily this all can be derived fairly easily by simply looking at the carnot engine diagram I drew above. It makes sense that the heat going in is equal to the heat and work coming out. It makes sense that the ratio of heats is equal to the ratio of temperatures. As long as you know what efficiency is, all of this naturally falls out from pluggin-and-chuggin.

I hope that this helps and doesn't make this more confusing, just thought I'd try to wrap up the entire subject of efficiency real quick lol.

Answer 9

:o thanks for describing this so thoroughly. :D

Answer 10

Yeah, if you'd like me to explain more I'm happy to help anyone interested in understanding. =D

Answer 11

I mean, explain as far as what might not have made sense or if you didn't understand how I was able to make a step or whatever, I'll do my best to explain it better for you if you need.

Answer 12

how can u tell if you're given Qc or Qh?

Answer 13

Ah, well a carnot engine always takes in heat from a higher temperature to do work.

Imagine it like a steam engine on a train. The guy heats up the steam, (qh) and then the wheels move (w), and then the steam comes off into the open air (qc).

So when you see that it says, "Produces x amount of heat" you know that that's qc since it comes from it, not the heat that you put into it, which is qh.

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As a side note, you can reverse the carnot cycle to give you refrigeration. By putting work into the carnot cycle, it takes heat from indoors and pushes it outside. If this helps you understand, then good. If not, don't worry about this.

Answer 14

ohhh ok, thanks. reading isn't my strong point :'(

Answer 15

It's ok, thermodynamics is kind of weird and hard to get used to. It's like they throw all these things at you that have a physical meaning but they don't explain them very well. Like, what the hell is enthalpy? That used to mess me up for a long time trying to sort out what all the variables actually meant.