Question

A Carnot engine working between 400oC and 40oC produces 130 kJ of work. Determine:
i. The engine thermal efficiency
ii. The heat added

Answer 1

To find the thermal efficiency of the Carnot engine, we can use the formula:

Efficiency = (1 - (Tc/Th)) * 100

Where:
Tc = temperature of the cold reservoir
Th = temperature of the hot reservoir

In this case, Tc = 40°C (273.15 + 40 = 313.15 K) and Th = 400°C (273.15 + 400 = 673.15 K).

Efficiency = (1 - (313.15/673.15)) * 100
Efficiency = (1 - 0.4646154) * 100
Efficiency ≈ 53.54%

Therefore, the engine has a thermal efficiency of approximately 53.54%.

To find the heat added to the engine, we can use the formula:

Efficiency = (Work output / Heat input) * 100

Given that the work output is 130 kJ, we can rearrange the formula to solve for heat input:

Heat input = (Work output / Efficiency) * 100

Heat input = (130 / 53.54) * 100
Heat input ≈ 242.72 kJ

Therefore, the heat added to the engine is approximately 242.72 kJ.