Query Assignment 8

course Phy 202

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Physics II

06-19-2006

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10:23:18

prin phy and gen phy problem 15.19 What is the maximum efficiency of a heat engine operating between temperatures of 380 C and 580 C?

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RESPONSE -->

I changed the temperatures from degrees Celsius to Kelvin:

580C = 853 K

380C = 653K

Then I used the formula:

e = (TH - TL)/TH

e = (853-653)/853

e = .23

So, efficiency it 23 %

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10:23:37

The maximum possible efficiency is (T_h - T_c) / T_h, where T_h and T_c are the absolute max and min operating temperatures.

T_h is (580 + 273)K = 853 K and T_c is (380 + 273) K = 653 K, so the maximum theoretical efficiency is

max efficiency = (T_h - T_c) / T_h = (853 K - 653 K) / (853 K) = .23, approx.

This means that the work done by this engine will be not greater than about 23% of the thermal energy that goes into it.

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RESPONSE -->

Okay

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10:29:51

query gen phy problem 15.26 source 550 C -> Carnot eff. 28%; source temp for Carnot eff. 35%?

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RESPONSE -->

I could find the low temperature from using the formula

e = 1 - (T_L/T_H)

.28 = 1 - (T_L/823K)

593 K = T_L = 320 C

But after that I wasn't sure how to find the new temperature with the new effieciency. I wasn't sure if I was supposed to find the T_H by using the new efficiency and the T_L that I got as the answer for the first part. But this is what I tried:

e = 1 - (T_L / T_H)

.35 = 1 - (593K / T_H)

912 K = T_H

639 C = T_H

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10:30:33

** Carnot efficiency is eff = (Th - Tc) / Th.

Solving this for Tc we multiply both sides by Th to get

eff * Th = Th - Tc so that

Tc = Th - eff * Th = Th ( 1 - eff).

We note that all temperatures must be absolute so we need to work with the Kelvin scale (adding 273 C to the Celsius temperature to get the Kelvin temperature)

If Th = 550 C = 823 K and efficiency is 30% then we have

Tc =823 K * ( 1 - .28) = 592 K.

Now we want Carnot efficiency to be 35% for this Tc. We solve eff = (Th - Tc) / Th for Th:

Tc we multiply both sides by Th to get

eff * Th = Th - Tc so that

eff * Th - Th = -Tc and

Tc = Th - eff * Th or

Tc = Th ( 1 - eff) and

Th = Tc / (1 - eff).

If Tc = 576 K and eff = .35 we get

Th = 592 K / ( 1 - .35 ) = 592 C / .6 = 912 K, approx.

This is (912 - 273) C = 639 C. **

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RESPONSE -->

Okay, so I did it correctly.

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10:30:46

univ phy problem 20.44 (18.40 10th edition) ocean thermal energy conversion 6 C to 27 C

At 210 kW, what is the rate of extraction of thermal energy from the warm water and the rate of absorption by the cold water?

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RESPONSE -->

Gen Phys Student

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10:30:48

** work done / thermal energy required = .07 so thermal energy required = work done / .07.

Translating directly to power, thermal energy must be extracted at rate 210 kW / .07 = 30,000 kW. The cold water absorbs what's left after the 210 kW go into work, or 29,790 kW.

Each liter supplies 4186 J for every degree, or about 80 kJ for the 19 deg net temp change. Needing 30,000 kJ/sec this requires about 400 liters / sec, or well over a million liters / hour.

Comment from student: To be honest, I was suprised the efficiency was so low.

Efficiency is low but the energy is cheap and environmental impact in the deep ocean can be negligible so the process can be economical, if a bit ugly. **

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RESPONSE -->

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Good work. Let me know if you have questions.