Ideal Heat Engine: Input Temp Change, Exhaust Temp Change?

[cuddlylover]

An ideal heat engine operates with an input temperature of 327C and an exhaust temperature
of 27C. If the input temperature is lowered to 227C, by how much must be the exhaust
temperature be lowered to maintain the same eciency?Im using η= 1-(tc/th) that works out to 1-(300k/600k) = 0.5 then took 227c = 500k*0.5 =250 ∴ 1-(250k/500k)=0.5

So i come to -23c but that dose not seem right if someone can help me here would be a big help thanks

 

[BruceW]

That looks right to me. Why did you think it was incorrect? On another note, your working seems a bit unclear. I see you calculate the original efficiency, and I understand that bit of the working. But then I don't follow the rest of it.

 

[cuddlylover]

I worked out the original efficiency and then times the original efficiency by input temperature 2 to get the exhaust temperature 2.

Is that not right how would you do the working?

I was thinking it was incorrect base on a feeling there is a carnot limit of about 10C but i mite be wrong :)

 

[BruceW]

I worked out the original efficiency and then times the original efficiency by input temperature 2 to get the exhaust temperature 2.

Is that not right how would you do the working?

No, this is not the correct working. But it happens to get the right answer in this case just by coincidence. I think you need to take more time to rearrange the equations properly. You have two equations: old efficiency and new efficiency, and you know these are equal. How would you write this algebraically?

I was thinking it was incorrect base on a feeling there is a carnot limit of about 10C but i mite be wrong :)

there is no temperature limit (apart from absolute zero, but that's much less than 10C)

 

[Andrew Mason]

So i come to -23c but that dose not seem right if someone can help me here would be a big help thanks

You have to answer the question. The question asks by how much must the temperature of the exhaust be lowered, not to what temperature it must be lowered. Apart from that, I think you have the right idea.

AM

 

[BruceW]

Oh, that's right. That is the last step which I forgot about as well. Cuddlylover still needs to do the correct working also.

 

[cuddlylover]

How would i write and do this algebraically?

 

[Andrew Mason]

How would i write and do this algebraically?

Write the expression for efficiency of the engine in the second case in terms of the input and exhaust temperatures (using Qc for the exhaust temp). Set that to the efficiency of the engine in the first case. Solve for Qc.

AM