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Heat Engine/Thermodynamics

  • #1
103
0

Homework Statement



A heat engine is built to operate between temperatures of 1200 K and 300 K. It is used to lift a 30 kg mass at a constant velocity of 4 m/s.

a) Determine the power that the heat engine must supply to lift the mass.

b) Determine the maximum possible efficiency of the heat engine.

c) If the engine were to operate at the maximum possible efficiency, determine the following:
i. The rate at which the hot reservoir supplies heat to the engine.
ii. The rate at which heat is exhausted to the cold reservoir.


Homework Equations



P = W/t
e = 1 - T1/T2


The Attempt at a Solution



I figured out that (b) is 1 - (300/1200) = 75%.

For (a), there is no distance stated to figure out work (W = Fd), and there is no time to determine power (P = W/t). What am I missing?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
5
Power= rate of doing work. = Fd/t = fv.
 
  • #3
103
0
Power= rate of doing work. = Fd/t = fv.
Oh! So, P = Fv = (30 kg)(9.8 m/s^2)(4 m/s) = 1176 J/s.

So, if the power supplied to lift the mass is 1176 J/s, and the maximum possible efficiency is 75%, then the rate heat is removed from the hot reservoir.... Wouldn't that depend on the first law of thermodynamics?
[delta]U = Q + W

But how would you apply the equation exactly, and what would it signify?
 
  • #4
Andrew Mason
Science Advisor
Homework Helper
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325
Oh! So, P = Fv = (30 kg)(9.8 m/s^2)(4 m/s) = 1176 J/s.

So, if the power supplied to lift the mass is 1176 J/s, and the maximum possible efficiency is 75%, then the rate heat is removed from the hot reservoir.... Wouldn't that depend on the first law of thermodynamics?
[delta]U = Q + W

But how would you apply the equation exactly, and what would it signify?
You do not need to apply the first law here. You just have to apply the efficiency. The work output is 1176 watts (J/s) at 75% efficiency (efficiency = work out/energy in) so the energy (heat flow) input must be...?

AM
 
  • #5
103
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You do not need to apply the first law here. You just have to apply the efficiency. The work output is 1176 watts (J/s) at 75% efficiency (efficiency = work out/energy in) so the energy (heat flow) input must be...?

AM
So, given the equation e = W/QH...

.75 = (1176W)/QH

QH = 1568 W


And, for the rate at which heat is exhausted to the cold reservoir, does this also depend on an efficiency equation?
 
Last edited:
  • #6
djeitnstine
Gold Member
614
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75% = 75/100 = 0.75

for rate at which heat is exhausted note that W = QH-QC. So dW/dt = dQH/dt - dQC/dt
 
  • #7
103
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75% = 75/100 = 0.75

for rate at which heat is exhausted note that W = QH-QC. So dW/dt = dQH/dt - dQC/dt
Hmm... Unfortunately, this is a non-calc based course, so would you know of another approach?
 
  • #8
djeitnstine
Gold Member
614
0
dW/dt = Power

dQh/dt = rate of energy output from the hot resevior

or perhaps delta Qh/ delta t which is average energy over a period of time

similar argument for Qc
 
  • #9
103
0
dW/dt = Power

dQh/dt = rate of energy output from the hot resevior

or perhaps delta Qh/ delta t which is average energy over a period of time

similar argument for Qc
Yes, but unfortunately, this is an algebra-based course. Is there another method for finding the rate at which heat is exhausted to the cold reservoir?
 
  • #10
Andrew Mason
Science Advisor
Homework Helper
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325
Yes, but unfortunately, this is an algebra-based course. Is there another method for finding the rate at which heat is exhausted to the cold reservoir?
W = Qh-Qc

P = W/t = Qh/t - Qc/t

You know two of those terms. So find Qc/t

AM
 
  • #11
103
0
W = Qh-Qc

P = W/t = Qh/t - Qc/t

You know two of those terms. So find Qc/t

AM
W = QH - QC

392 W = 980 W - QC/t

QC/t = 588 W

Correct?
 
  • #12
Andrew Mason
Science Advisor
Homework Helper
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W = QH - QC

392 W = 980 W - QC/t

QC/t = 588 W

Correct?
I am not sure what you are doing here.

W/t = 1176 w
Qh/t = W/e = 1568 w

AM
 
  • #13
103
0
I am not sure what you are doing here.

W/t = 1176 w
Qh/t = W/e = 1568 w

AM
My apologies. I was working on two similar problems... that's why the values were different.

Thank you very much for your help! I appreciate it.

-Science.girl
 

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