The hot reservoir for a Carnot engine has a temperature of 924 K, while the cold
ID: 1473092 • Letter: T
Question
The hot reservoir for a Carnot engine has a temperature of 924 K, while the cold reservoir has a temperature of 646 K. The heat input for this engine is 5119 J. The 646 K reservoir also serves as the hot reservoir for a second Carnot engine. This second engine used the rejected heat of the first engine as input and extracts additional work from it. The rejected hear from the second engine goes into a reservoir that has a temperature of 285 K. Find the total work delivered by the two engines. The hot reservoir for a Carnot engine has a temperature of 924 K, while the cold reservoir has a temperature of 646 K. The heat input for this engine is 5119 J. The 646 K reservoir also serves as the hot reservoir for a second Carnot engine. This second engine used the rejected heat of the first engine as input and extracts additional work from it. The rejected hear from the second engine goes into a reservoir that has a temperature of 285 K. Find the total work delivered by the two engines.Explanation / Answer
Treat both engines as ideal reversible. The they operate at the maximum thermal efficiency , which is given by:
W / Q_in = 1 - T_cold / T_hot
For the first engine
= 1 - 646K / 924K = 0.3008
and for the second
= 1 - 285K / 646K = 0.5588
The work done by the first engine is
W = Q_in ·
it rejects the heat
Q_out = Q_in - W = Q_in ·(1 - )
The work done by the second engine is
W = Q_in · = Q_out · = Q_in ·(1 - ) ·
Therefore the total work done is:
W = W + W
= Q_in · + Q_in ·(1 - ) ·
= Q_in · ( + (1 - ) · )
= 5119J · ( 0.3008 + (1 - 0.3008) · 0.5588)
= 3539.8548 J
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