# Show that the change in entroy is

1. Mar 17, 2006

### endeavor

Show that the change in entropy for a cycle of a heat engine is
$$\Delta S = \frac{Q_{cold}}{T_{cold}} - \frac{Q_{hot}}{T_{hot}}$$

2. Mar 17, 2006

### Hootenanny

Staff Emeritus
Please show some working or thoughts...

3. Mar 17, 2006

### endeavor

$$W = Q_{in} - Q_{out} = Q_{hot} - Q_{cold}$$
or that
$$\Delta S = S_{f} - S_{i}$$
But I'm not sure where to go from here...

4. Mar 17, 2006

### Andrew Mason

You are to assume an isothermal heat transfer from the hot register to the gas and an isothermal flow from the gas to the cold register.

The change in entropy for the hot register in the transfer from the hot register to the gas is:

$$dS_h = -dQ_h/T_h$$

Similarly, the change in entropy of the cold register in extracting the heat from the gas to the cold register results in a change of entropy to the cold register of:

$$dS_c = +dQ_c/T_c$$

The total change in entropy of the system (hot register + cold register) is:

dS_{total} = dS_h + dS_c = dQ_c/T_c-dQ_h/T_h[/tex]

AM