Heat engine (application of the second law of thermodynamics) – problems and solutions

1. Heat input Q_H = 3000 Joule and heat output Q_L = 1000 Joule. What is the efficiency of the heat engine?

Known :

Heat input (Q_H) = 3000 Joule

Heat output (Q_L) = 1000 Joule

Work done by the engine (W) = 3000 – 1000 = 2000 Joule

Wanted: Efficiency of the heat engine (e)

Solution :

[irp]

2. A heat engine produces 2000 Joule of mechanical work and the engine discharges heat to the environment at a rate of 500 Joule. What is the efficiency of the heat engine?

Known :

The work is done by the engine (W) = 2000 Joule

Heat output (Q_L) = 5000 Joule

Heat input (Q_H) = 2000 + 5000 = 7000 Joule

Wanted: Efficiency (e)

Solution :

[irp]

3. A heat engine has an efficiency of 30%. If the engine produces 10,000 Joule of mechanical work, how much heat is discharged as waste heat from this engine?

Known :

Efficiency (e) = 30 % = 30/100 = 0.3

The work is done by engine (W) = 3,000 Joule

Wanted : Heat output (Q_L)

Solution :

Heat output (Q_L) = heat input (Q_H) – work is done by engine (W)

Q_L = 10,000 Joule – 3,000 Joule

Q_L = 7,000 Joule