Work done by a 20% efficient heat engine

[kokodile]

I had an exam last week and I just got it back today. On the exam was a question that I got wrong even though his wording was terrible (he's from India) and I feel that it was not clearly expressed what he was saying. The question is: "A heat engine is 20% efficient. If it absorbs 500 J of heat from reservoir. What is the work done by engine and heat rejected to the cold reservoir?"

I would like to see what answers you all come up with
Relevant equations
W.D=Qh-Qc
Efficiency=1-(Qc/Qh)

 

[alivedude]

I had an exam last week and I just got it back today. On the exam was a question that I got wrong even though his wording was terrible (he's from India) and I feel that it was not clearly expressed what he was saying. The question is: "A heat engine is 20% efficient. If it absorbs 500 J of heat from reservoir. What is the work done by engine and heat rejected to the cold reservoir?"

I would like to see what answers you all come up with
Relevant equations
W.D=Qh-Qc
Efficiency=1-(Qc/Qh)

Let us first see your answer and his respond.

 

[phinds]

I would like to see what answers you all come up with

No, you have to show YOUR work and we'll see if we can see any error in it.

 

[AbhinavJ]

Yeah, show your work first

 

[kokodile]

Let us first see your answer and his respond.

Well the reason i didn't put what my answer was is because I want to see what you think the question is asking. Let's just say that I thought 500 was Qc. From there, I solved the problem correctly if 500 was Qc.

 

[AbhinavJ]

Well the reason i didn't put what my answer was is because I want to see what you think the question is asking. Let's just say that I thought 500 was Qc. From there, I solved the problem correctly if 500 was Qc.

By Qc = 500 you imply that the Work done by the engine is 0. I can't see it being right.
Can you show how you got it to be 500?

P. S The wording seems more than fine to me

 

[alivedude]

Well the reason i didn't put what my answer was is because I want to see what you think the question is asking. Let's just say that I thought 500 was Qc. From there, I solved the problem correctly if 500 was Qc.

Well, we aren't allowed to solve problems for other members so I suggest that you write out your whole solution and what your professor said about it, I can't imagine a better way to do it :)

 

[kokodile]

By Qc = 500 you imply that the Work done by the engine is 0. I can't see it being right.
Can you show how you got it to be 500?

Because it says the heat 'absorbed' is 500 J and heat can only go from high to low, right? So if I thought the given 500 J was Qc then I got 625 solving for Qh and then the work done was 125.

 

[kokodile]

And my professor was trying to explain to me why the given 500 J is Qh but I couldn't understand why because it says 500 J was absorbed.

 

[AbhinavJ]

And my professor was trying to explain to me why the given 500 J is Qh but I couldn't understand why because it says 500 J was absorbed.

Your professor is absolutely correct. See, how a heat engine works is that it absorbs heat from the hot reservoir, uses part of it to do some work and rejects the remaining heat to the cold reservoir.

https://lh5.googleusercontent.com/proxy/KjKcuCkFTlJb7OvC0ZHGzibhvIDCxlbEi38C4DLxxBYHH8PNE6WqyTb3iG_-hgQIfKynsIqpPRY7b5MCpieNlUVCMuFrLuRrFObbo7S3AKtE5vYjD95cdw0BS5B8dhGSJRNk2y7P3HZalIB0dGBkF-Ba=w300-h300-nc

So by absorbed 500J, the question gave us information about the heat taken from the hot reservoir.

And i have no idea how you got Qc, Qh and work done. Can you write the equations?

 

[kokodile]

But if heat is taken from the hot reservoir by another body, then wouldn't that be Qc?

I posted the equations in the original question.

Efficiency=1-(Qc/Qh)
So .2=1-(500/Qh) ( This is what I did.)
So from that equation I got Qh=625 J.
And if work done=Qh-Qc then 625-500 is 125 J of work done.

 

[AbhinavJ]

But if heat is taken from the hot reservoir by another body, then wouldn't that be Qc?

What do you mean by Qh and Qc?

 

[kokodile]

What do you mean by Qh and Qc?

Qh is the amount of heat rejected by the hot reservoir. Qc is the amount of heat absorbed by cold reservoir from hot reservoir. This is how I learned it.

 

[AbhinavJ]

Qh is the amount of heat rejected by the hot reservoir. Qc is the amount of heat absorbed by cold reservoir from hot reservoir. This is how I learned it.

Okay, so isn't the heat taken by the engine equal to the heat rejected by the reservoir?

Consider your attached file, is their any other way that the heat is being dissipated or lost other than being absorbed by the engine?

 

[kokodile]

Okay, so isn't the heat taken by the engine equal to the heat rejected by the reservoir?

Consider your attached file, is their any other way that the heat is being dissipated or lost other than being absorbed by the engine?

No, it's not equal. There's the hot reservoir, and then the engine (which is the part that does work), and then the cold reservoir. So heat is ejected from the hot reservoir (Qh) to the engine. The engine uses some of the heat to do work and then ejects the rest of the heat to the cold reservoir (Qc). Here's a more specific diagram similar to what my professor used to teach us.

So the hot reservoir ejects the heat and then whatever heat the engine does not use is absorbed by the cold reservoir. This is why I assumed that the given 500 Joules was Qc because it said the heat was *absorbed*, which I took as "absorbed by the cold body" which, apparently, was wrong.

 

[AbhinavJ]

No, it's not equal.

The heat given by the hot reservoir is equal to the heat taken by the engine.

Glad you found your mistake, does your answer match now?

 

[kokodile]

The heat given by the hot reservoir is equal to the heat taken by the engine.

Glad you found your mistake, does your answer match now?

No, I still don't get it. I never said that Qh and Qc were equal from the start. I always knew that. My problem is, 500 J was *absorbed*, but if something is absorbed by something else (since heat only travels from high to low temperature) that means it had to have been to a cold body from a hot body. So if something absorbed heat that means the body that absorbed it was the cold reservoir, which is Qc, and the body that give the cold reservoir the heat is Qh. This is what I'm confused about.

 

[AbhinavJ]

No, I still don't get it. I never said that Qh and Qc were equal from the start. I always knew that. My problem is, 500 J was *absorbed*, but if something is absorbed by something else (since heat only travels from high to low temperature) that means it had to have been to a cold body from a hot body. So if something absorbed heat that means the body that absorbed it was the cold reservoir, which is Qc, and the body that give the cold reservoir the heat is Qh. This is what I'm confused about.

Every engine has a working fluid inside it which is responsible for all the things the engine does. It is the fluid which absorbs heat from the hot reservoir and also the one to reject heat into the cold reservoir. Let's talk about the basic heat engine, A Steam engine.
Water here is the working fluid.

The coal burns and heats a boiler full of water to make steam. Steam from
the boiler is piped into the cylinder, causing
the piston to move first one way then the other this is where the work is done and then the steam is ejected into the atmosphere which acts as a cold Reservoir.

 

[kokodile]

Every engine has a working fluid inside it which is responsible for all the things the engine does. It is the fluid which absorbs heat from the hot reservoir and also the one to reject heat into the cold reservoir. Let's talk about the basic heat engine, A Steam engine.

A fire where the coal burns and heats a boiler full of water that heats up to make steam. A cylinder and piston, rather like a bicycle
pump but much bigger. Steam from
the boiler is piped into the cylinder, causing
the piston to move first one way then the other this is where the work is done and then the steam is ejected into the atmosphere which acts as a cold Reservoir.

So in this case, I shouldn't have taken the hot reservoir into account? Only the engine and the atmosphere? So the atmosphere was the "cold reservoir" and the engine was the hot reservoir?

 

[DrClaude]

To complement the answer @AbhinavJ, you have to see it from the point of view of the engine (or working substance). This is standard in thermodynamics.

Also, you can just simply parse the sentences:
"A heat engine is 20% efficient. If it absorbs 500 J of heat from reservoir."
It stands for the engine. So the heat must correspond to what goes into the engine. Also, the heat comes from the reservoir. Only the engine is connected to the reservoirs; the reservoirs are not connected to each other.

"What is the work done by engine and heat rejected to the cold reservoir?"
The verb used for the transfer to the cold reservoir is rejected, so clearly taken from the point of view of the engine.

 

[AbhinavJ]

So in this case, I shouldn't have taken the hot reservoir into account? Only the engine and the atmosphere? So the atmosphere was the "cold reservoir" and the engine was the hot reservoir?

The fire was the hot reservoir

 

[kokodile]

To complement the answer @AbhinavJ, you have to see it from the point of view of the engine (or working substance). This is standard in thermodynamics.

Also, you can just simply parse the sentences:
"A heat engine is 20% efficient. If it absorbs 500 J of heat from reservoir."
It stands for the engine. So the heat must correspond to what goes into the engine. Also, the heat comes from the reservoir. Only the engine is connected to the reservoirs; the reservoirs are not connected to each other.

"What is the work done by engine and heat rejected to the cold reservoir?"
The verb used for the transfer to the cold reservoir is rejected, so clearly taken from the point of view of the engine.

Right, but if the heat is coming from the hot reservoir and the engine is absorbing the 500 J from the hot reservoir, then doesn't that still make it sound like the 500 J is Qc?

 

[AbhinavJ]

Right, but if the heat is coming from the hot reservoir and the engine is absorbing the 500 J from the hot reservoir, then doesn't that still make it sound like the 500 J is Qc?

No.

 

[CWatters]

+1

The question mentions a heat engine and says _it_ absorbs 500J. It seems clear that the _it_ is the engine not the cold reservoir.

Eg 500Joules of "fuel" goes into the engine. 20% is turned into useful work and 80% ends up in the cold reservoir