A Carnot engine is operated between two heat reservoirs at temperatures 520 K and 300 K.(a) If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K?(b) How much mechanical work is performed by the engine during each cycle?(c) What is the thermal efficiency of the engine?



Answer :

The thermal efficiency of the  Carnot engine is operated between two heat reservoirs at temperatures 520 K and 300 K is 42.3 %

A). 3692.8 J  joules per cycle does it reject to the reservoir at 300 K

(B)   2707.2 Joules mechanical work is performed by the engine during each cycle.

(C)  the thermal efficiency of the engine is 42.3 %.

Calculation:

Given,

temperature of hot resorvoir, Th = 520 K

temperature of cold resorvoir, Tc = 300 K

A) now Apply, Qin = W + Qout

=> Qout = Qin - W

= 6400 - 2707.2

= 3692.8 J

B)  Apply, e = W/Qin

=> W = Qin*e

= 6400*0.423

= 2707.2 J

c) efficiency of cornot engine, e = 1 - Tc/Th

= 1 - 300/520

= 0.423

= 42.3 %

A Carnot heat engine  is a heat engine that operates according to the Carnot cycle. The basic model of this engine was developed in 1824 by Nicolas Leonardo Sadi his Carnot. The model of the Carnot engine was graphically extended by Benoît-Paul-Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, leading to the basic thermodynamic concept of entropy. The Carnot engine is the most efficient heat engine theoretically possible. [3] Efficiency depends only on the absolute temperature of the hot and cold regenerators in which it operates.

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