Heat Q flows spontaneously from a reservoir at 383 K into a reservoir

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In summary, the problem involves the spontaneous flow of heat Q from a reservoir at 383 K into a reservoir at a lower temperature T. 30% of Q is rendered unavailable for work when a Carnot engine operates between the two reservoirs. The efficiency of the Carnot engine can be calculated using the equation e = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir (234 K) and Th is the temperature of the hot reservoir (T). To solve for T, the equation can be rearranged to T = Tc / (1 - e). However, there may be some confusion in the problem regarding the actual amount of heat taken in
  • #1
copitlory8
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Heat Q flows spontaneously from a reservoir at 383 K into a reservoir that has a lower temperature T. Because of the spontaneous flow, thirty percent of Q is rendered unavailable for work when a Carnot engine operates between the reservoir at temperature T and a reservoir at 234 K. Find the temperature T.

I have absolutely no idea. Please help me. I am getting desperate. I have to pull up my failing physics grade or else i will pretty much be disowned by my family.
 
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  • #2
copitlory8 said:
Because of the spontaneous flow, thirty percent of Q is rendered unavailable for work

Given this, what would the efficiency of the Carnot Engine?

When you get that, what is the expression for efficiency of a Carnot Engine?
 
  • #3
the efficiency i guess is 2/3.
e=1-(Tc/Th)
 
  • #4
so what next?
 
  • #5
copitlory8 said:
the efficiency i guess is 2/3.

How did you get 2/3 ?

copitlory8 said:
e=1-(Tc/Th)

So when you get 'e' Th=T, and you were given Tc, can you get T?
 
  • #6
i got 2/3 because it says that 1/3 is unavailable therefore 2/3 is available
 
  • #7
copitlory8 said:
i got 2/3 because it says that 1/3 is unavailable therefore 2/3 is available

That thinking is correct but thirty percent is not the same as 1/3.
 
  • #8
oh no! I am lost again what is the th?
 
  • #9
so the efficiency is actually .7
 
  • #10
copitlory8 said:
so the efficiency is actually .7

Right so, what is T?
 
  • #11
there are two Ts in the problem. do i use the higher one for Th?
 
  • #12
copitlory8 said:
there are two Ts in the problem. do i use the higher one for Th?

You are only considering the two temperatures associated with the Carnot engine, the high temperature T and the lower temperature 234 K.
 
  • #13
so i use 234K?
 
  • #14
copitlory8 said:
so i use 234K?

Yes.
 
  • #15
so let me get this straight .7(234)=T where T is the answer I am looking for? this seems too simple
 
  • #16
copitlory8 said:
so let me get this straight .7(234)=T where T is the answer I am looking for? this seems too simple

e=1- (Tc/T), so you '0.7' would be '0.3'.

Nothing is being done to the heat when it is moving from 384K to T, so I don't think you'd need to worry about that for now.
 
  • #17
so .3=1-(234/t)
 
  • #18
copitlory8 said:
so .3=1-(234/t)

No, 0.7 = 1 -(Tc/T)

when you rearrange you'd get the '0.3'.
 
  • #19
alright i think i almost got this. so the T i am trying to solve for is equal to Tc/.3
 
  • #20
copitlory8 said:
alright i think i almost got this. so the T i am trying to solve for is equal to Tc/.3

Yes and you know th vaue of Tc.
 
  • #21
then what is the number 383 K for?
 
  • #22
copitlory8 said:
then what is the number 383 K for?

Not too sure why it was given in the problem.
 
  • #23
i did 234/.3=780 and got the wrong answer.
 
  • #24
Yes I realized, I've asked the other HW helpers to see if they can clarify my error in thinking.
 
  • #25
thanks
 
  • #26
copitlory8 said:
Heat Q flows spontaneously from a reservoir at 383 K into a reservoir that has a lower temperature T. Because of the spontaneous flow, thirty percent of Q is rendered unavailable for work when a Carnot engine operates between the reservoir at temperature T and a reservoir at 234 K. Find the temperature T.
Odd problem :uhh:

Anyway, here is my understanding of the problem. A certain amount of thermal energy Q flows from the 383 K reservoir into the reservoir at T. Then a certain different amount of thermal energy (let's call it Q') is transferred from that reservoir, through a Carnot engine, to a reservoir at 234 K. Hopefully you can agree that it makes sense that Q' < Q, although I'm not sure if/how it can be proven that this condition must hold, and that 234 K < T < 383 K.

Now, the problem says that 30% of Q is rendered unavailable for work in the Carnot engine. Here is where it gets confusing. One way to read that is that the spontaneous flow brings the total amount of energy unavailable for doing work up to 30% of Q. This implies that the remaining 70% of Q is available and is used for doing work in the Carnot engine - basically that W = 0.7 Q. So you have W for the heat engine, in relation to Q, but not in relation to Q', which is the actual amount of heat taken in by the engine. To figure out the efficiency of the engine (and thus the temperature of its hot reservoir), you would have to relate Q to Q'.

The other possible reading I see is that 30% of the thermal energy Q is removed from the flow before the energy ever reaches the engine. This would be saying that Q - Q' = 0.3 Q. But with this reading, you have no information about the operation of the engine itself - you don't know anything about its work output or its efficiency. I don't really see where you would go from there.
 
  • #27
so i should just give up and fail
 
  • #28
copitlory8 said:
so i should just give up and fail
Why would you do that?
 
  • #29
i should just give up because this problem is so ridiculous, not even my awesome physics teacher can solve it after i spent 45 minutes with him on it.
 
  • #30
It seems quite unreasonable for your teacher to assign you and expect you to solve a homework problem which he himself can't do. But we're not here to tell you what to do, only to help you understand the physics.
 
  • #31
well i understand but my teacher is really smart. and the way webassign works is that is has a huge databank of questions released from my textbook publisher and it picks questions randomly. so my teacher hasn't even seen all the questions so once in a while a tough one appears such as this one. can someone seriously just tell me the solution
 
  • #32
No, we will not just give you the solution. If you think you deserve to be just given the answer, ask your teacher. Instructors who use WebAssign have access to a complete answer key, and in some cases explanations of how the problems are solved.

As long as you are willing to continue to make an effort on the problem, we can do our best to guide you through it.
 

1. What is meant by "heat Q flows spontaneously"?

When heat Q flows spontaneously, it means that there is a natural tendency for heat to move from a warmer object or system to a cooler one. This movement occurs without any external force or energy being applied.

2. Why is the temperature of the reservoir at 383 K significant?

The temperature of the reservoir at 383 K is significant because it represents the source of heat energy. In this scenario, the reservoir at 383 K is the warmer object or system from which heat is flowing into the cooler reservoir.

3. What factors influence the rate at which heat Q flows?

The rate at which heat Q flows is influenced by several factors, including the temperature difference between the two reservoirs, the type of material the heat is flowing through, and the surface area and thickness of the material.

4. Is this process reversible?

No, this process is not reversible. Heat naturally flows from a warmer object to a cooler one, and it requires external energy or work to reverse this flow.

5. How is this principle applied in real-world situations?

This principle is applied in various real-world situations, such as in refrigerators and air conditioners, where heat is removed from a cooler space and released into a warmer space. It is also important in understanding energy transfer in thermal power plants and the Earth's climate system.

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