Question

A real heat engine working between heat reservoirs at 955 K and 655 K produces 565 J of work per cycle for a heat input of 2080 J. Compare the efficiency of this real engine to that of an ideal (Carnot) engine.

% of ideal

Answer 1

The efficiency of a real heat engine working between heat reservoirs at 955 K and 655 K is 27.16%, while the efficiency of an ideal (Carnot) engine is 31.51%. The real engine is less efficient than the ideal (Carnot) engine.

Step-by-step explanation:

The efficiency of a heat engine is determined by the ratio of work output to heat input. To compare the efficiency of the real engine to that of an ideal (Carnot) engine, we can use the formula:

Efficiency = (Work output / Heat input) × 100%.

For the real engine, the work output is 565 J and the heat input is 2080 J. Plugging these values into the formula, we get:

Real engine efficiency = (565 / 2080) × 100% = 27.16%.

For an ideal (Carnot) engine, the efficiency is given by the formula:

Carnot engine efficiency = 1 - (T₃ / T₁), where T₃ is the temperature of the cold reservoir and T₁ is the temperature of the hot reservoir. In this case, T₃ = 655 K and T₁ = 955 K. Plugging these values into the formula, we get:

Carnot engine efficiency = 1 - (655 / 955) = 31.51%.

Therefore, the efficiency of the real engine is 27.16% and the efficiency of the ideal (Carnot) engine is 31.51%. The real engine is less efficient than the ideal (Carnot) engine.