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Answer :
Answer:
The work done by the carnot engine per cycle is 1318.31 J
Explanation:
Given;
high temperature reservoir, Th = 435 k
temperature of river water, Tl = 280 k
heat energy absorbed per cycle, Q = 3700 J
Determine the work done per cycle is calculated as;
[tex]W = Q(1-\frac{T_l}{T_h} )[/tex]
Where;
W is the work done
Q is the absolute heat absorbed per cycle
Tl is the temperature of the cold liquid
Th is the temperature of the hot reservoir
[tex]W = Q(1-\frac{T_l}{T_h} )\\\\W = 3700(1 - \frac{280}{435} )\\\\W = 3700 (1-0.6437)\\\\W = 1318.31 \ J[/tex]
Therefore, the carnot engine operating at the given conditions, performs 1318.31 J work per cycle.
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Final answer:
The Carnot engine performs 1318.31 J of work per cycle when operating between temperatures of 280 K and 435 K with an efficiency of 35.63%, absorbing 3700 J of heat per cycle from the hot reservoir.
Explanation:
The question asks about the work performed by a Carnot engine operating between two different temperatures. To find the amount of work done per cycle by the Carnot engine, we can use the efficiency formula for a Carnot engine, which is:
Efficiency (η) = 1 - (Tc / Th)
Where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. In this case, Tc is 280 K and Th is 435 K. The engine absorbs 3700 J of heat (Qh) each cycle from the hot reservoir. First, let's calculate the efficiency:
Efficiency (η) = 1 - (280 K / 435 K) = 0.3563 (or 35.63%)
Next, we determine the work (W) done using the formula:
W = η × Qh = 0.3563 × 3700 J = 1318.31 J
Therefore, the Carnot engine performs 1318.31 J of work per cycle.
