A gas within a piston-cylinder assembly executes a Carnot power cycle during whi

Question

A gas within a piston-cylinder assembly executes a Carnot
power cycle during which the isothermal expansion occurs
at Th=600 K and the isothermal compression occurs at
Tc=300K

Determine
(a) the thermal efficiency.
(b) the percent change in thermal efficiency if Th increases
by 15% while Tc remains the same.
(c) the percent change in thermal efficiency if Tc decreases
by 15% while Th remains the same.
(d) the percent change in thermal efficiency if Th increases
by 15% and Tc decreases by 15%.

Moran, Michael J.; Shapiro, Howard N.; Boettner, Daisie D.; Bailey, Margaret B. (2014-04-18). Fundamentals of Engineering Thermodynamics, 8th Edition (Page 286). Wiley. Kindle Edition.

Explanation / Answer

(a) Efficiency = 1-(Tc/Th) = 1-(300/600) = 0.5 or 50%

(b) Th = 600*1.15 = 690 K

Efficiency = 1-(Tc/Th) = 1-(300/690) = 0.565 or 56.5%

% increase = 6.5%

(c) Tc = 300*0.85 = 255 K

Efficiency = 1-(Tc/Th) = 1-(255/600) = 0.575 or 57.5%

% increase = 7.5%

(d)  Th = 600*1.15 = 690 K

Tc = 300*0.85 = 255 K

Efficiency = 1-(Tc/Th) = 1-(255/690) = 0.630 or 63%

% increase = 13%

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