answer the above one and there is hint down ------ A Carnot engine has an effici
ID: 2156670 • Letter: A
Question
answer the above one and there is hint down
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A Carnot engine has an efficiency of 35. 3% when the hot reservoir temperature is 420 degree C. If we want to improve the efficiency to 42. 6%, what should be the temperature of the hot reservoir, assuming everything else remains unchanged? Answer in units of degree C A Carnot engine has an efficiency of 26. 1 % when the hot reservoir temperature is 368degree C. If we want to improve the efficiency to 15. 7%, what should be the temperature of the hot reservoir, assuming everything else remains unchanged? Correct answer: 288. 921degree C. Let: epsilon 1 = 26. 1% = 0. 261, epsilon 2 = 15. 7% = 0. 157, and Th1 = 368degree C. Carnot efficiencies for both cases are epsilon 1 = 1 - Tc / Th1 Tc = Th1(1 - epsilon 1) and epsilon 2 = 1 - Tc / Th2Explanation / Answer
First of all, your hint is misleading; the book is wrong. Never do Carnot efficiency problems in Celsius; always convert to Kelvin first, then convert back if necessary. The ratios won't work in Celsius.
420 deg Celsius is 693.15 K.
= 1 - Tc/Th and we need Tc; solving for that variable,
Tc = Th(1 - ) = (693.15 K)(1 - 0.353) = 448.47 K
Given that, we need to solve for Th if our new is 0.426
Th = Tc/(1 - ) = (448.47 K)/(1 - 0.426) = 781.303 K
which is 508.15 degrees Celsius.
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