College

A Carnot engine operates between a high-temperature reservoir at 435 K and a river with water at 280 K. If it absorbs 3700 J of heat each cycle, how much work per cycle does it perform?

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.

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.