How to Calculate Carnot Efficiency of a Steam Engine

Question:

What is the Carnot efficiency of a steam engine that utilizes 547°C steam and exhausts it at 274°C?

Answer:

The Carnot efficiency of a steam engine that uses 547°C steam and exhausts it at 274°C is 33.33%.

To calculate the Carnot efficiency of a steam engine, we can use the formula:

Carnot Efficiency = 1 - (Tc/Th)

Where:

- Tc is the absolute temperature of the cold reservoir (274°C + 273.15 = 547.15 K).

- Th is the absolute temperature of the hot reservoir (547°C + 273.15 = 820.15 K).

Now, we plug these values into the formula:

Carnot Efficiency = 1 - (547.15/820.15) = 1 - 0.6667 ≈ 0.3333.

To express it as a percentage, we multiply by 100:

Carnot Efficiency ≈ 0.3333 * 100% ≈ 33.33%.

Therefore, the Carnot efficiency of this steam engine is approximately 33.33%.