# Heat engine

1. Jan 19, 2005

### Haftred

how can I find efficiency of heat engine operating between two differenct temperatures?

2. Jan 19, 2005

### Andrew Mason

Thermal efficiency would be defined as useful energy (work) output/ energy (heat) input:

$$\eta = \frac{W}{Q_H}$$

Since according to the first law: $\Delta Q = \Delta U + W$ where $\Delta U$ is 0 over one complete cycle, you have simply:

$\Delta Q = W = Q_H - Q_C$ where $Q_H$ is the heat input and $Q_C$ is the heat output.

So, efficiency is:

$$\eta = \frac{Q_H - Q_C}{Q_H} = 1 - \frac{Q_C}{Q_H}$$

Now the hard part is to determine what those heats are. To do this, you have to analyse the PV diagram for the engine cycle.

For the Carnot cycle (ideal) the efficiency is a function of temperatures, since all heat is input at constant temperature $T_H$ and output at constant temperature $T_C$.

$$\eta = 1 - \frac{T_C}{T_H}$$

AM

Last edited: Jan 20, 2005