Problem — Energy balance of an engine

Engine balance. Explain the energy balance of a car travelling at constant speed on flat ground: where does the chemical energy of the fuel end up? Give at least three dissipation channels.

Solution

Starting point: constant speed. On flat ground at constant speed the car neither accelerates nor changes height, so

$\Delta E_k = 0 \qquad \Delta E_p = 0$

No energy accumulates as motion or as height: all the fuel’s chemical energy ends up, sooner or later, dispersed into the environment as heat. The balance describes how it is distributed.

The channels (typical values for a combustion engine):

1. Direct engine heat ($\sim 60$–$70\%$). Combustion is a thermal process with limited efficiency: most of the energy leaves as heat in the exhaust gases and coolant. This is the dominant share.
2. Useful mechanical work ($\sim 25$–$30\%$). Moves the car, but at constant speed it only serves to overcome resistances: rolling friction of the tyres and, above all, air resistance (which grows with $v^2$). This work too therefore becomes heat in the environment.
3. Accessories ($\sim 5\%$). Alternator, air conditioning, pumps, electronics. Again energy that ends up as heat.

Summary of the balance:

$\ev{E_\text{chemical} \to \underbrace{Q_\text{engine}}_{\sim 65\%} + \underbrace{W_\text{mechanical}}_{\sim 27\%} + \underbrace{E_\text{accessories}}_{\sim 5\%} \ \to\ \text{all heat}}$

Physical reading. At cruising speed the car is a machine that converts chemical energy into ambient heat, passing through a small fraction of mechanical work that only serves to sustain motion against friction. The low overall efficiency ($\sim 25\%$) is a consequence of the second law, not a design flaw.

Collegamenti

Argomenti: Work and energy Concetti: Thermal energy from friction Competenze: Bubble energy balance