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# Physics, heat: What is its maximum theoretical efficiency?

1)One of the most efficient engines ever built is a coal-fired steam turbine in the Ohio valley, driving an electric generator as it operates between 1870°C and 430°C.

(a) What is its maximum theoretical efficiency?

%

(b) Its actual efficiency is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.4 105 J of energy each second from the hot reservoir?

kW

2) A 70-kg log falls from a height of 28 m into a lake. If the log, the lake, and the air are all at 303 K, find the change in entropy of the Universe during this process.

J/K

### 4 Answers

- kirchweyLv 71 decade agoFavorite Answer
1A. Max. theoretical (Carnot) efficiency = 1-T(cold)/T(hot) = 67.2 %. (T(cold) and T(hot) are of course in deg K.)

1B. That one you can do. 0.42*1.4E5.

2. The simplest solution (see ref.) is ΔS = ΔQ/T = mgh/T = 70*9.8*28/303 J/K.

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- Anonymous6 years ago
Adding onto Kirchwey's answer, I will take his advice and work out the problems.

1a) 1-(Tc/Th) = 1 - ((430+273) / (1870+273)) = 1 - (703 / 2143) = 0.671955203 (which is about 67.2%)

1b) Power = 0.42*1.4105E5 = 59241 J/s = 59241 W = 59.241 kW

2a is not applicable in Serway, Physics, 7th edition.

- Nurain Syahirah4 years agoReport
for the 1(b), whis formula you use?

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- tippettsLv 43 years ago
in basic terms calculate the theoretical efficiencies for the two situations (you ought to apply absolute temperatures): Eff1 = a million - (298/423) = one hundred twenty five/423 Eff2 = a million - (298/773) = 475/773 Eff2 / Eff1 = 475/773 * 423/one hundred twenty five = 2.a million So it will improve through a piece of two.a million

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- Anonymous1 decade ago
I liked the 2) part

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