Thermodynamics and Engine Efficiency

How can we calculate the work done and heat exhausted per cycle based on the engine's thermal efficiency?

Given the power output of a car engine is 400 kW running at 2800 rpm, with a thermal efficiency of 40.0%, what is the work done and heat exhausted per cycle?

The power output of the engine is 400 kW, which translates to 8 kJ of work done per cycle. The heat exhausted per cycle is 12 kJ.

The first law of thermodynamics states that the work done by the engine is equal to the heat input minus the heat output. By assuming the engine operates on a Carnot cycle, we can determine the thermal efficiency, given by:

Efficiency = W / Q_in = 1 - Q_out / Q_in

Where W is the work done per cycle, Q_in is the heat input per cycle, and Q_out is the heat output per cycle.

Since the power output of the engine is known to be 400 kW, the work done per cycle is calculated to be 8 kJ. To find the heat input per cycle, we use the equation:

Q_in = W / efficiency = 8 kJ / 0.4 = 20 kJ

Similarly, to find the heat output per cycle, we use the equation:

Q_out = Q_in - W = 20 kJ - 8 kJ = 12 kJ

Therefore, the work done per cycle is 8 kJ, and the heat exhausted per cycle is 12 kJ.

By understanding these calculations, we can further enhance the efficiency of engine performance and optimize energy usage.