# Heat Engine Calc confirmation

1. Nov 23, 2006

### S_fabris

Hey i have a heat engine that operates in a Carnot cycle between 354.05K and 711.15K, it absorbs 22415J of energy per cycle from hot resevoir. The duration of each cycle is 0.98s.
First question was to find the mechanical power output...i calculated this and got W = Qh - Qc = 22415 - 11159.43 = 11255.57 J/0.98s = 11,49kW

the next question asks how much energy does it expel in each cycle by heat in units of kJ..

everywhere I look it says to use Qc = Qh - W which gives me 11 159.43J is this right?? 11.16kJ?

this seems odd as an answer because it is the same answer as Qc.

Can anybody confirm this or steer me in right direction? thank you

2. Nov 23, 2006

### Andrew Mason

!! Qc IS the heat energy expelled in each cycle (ie the heat flowing to the cold reservoir.

For the Carnot cycle heat flows into and out of the reservoirs at constant temperature and there is 0 change in entropy. ie $\Delta S = Q_h/T_h - Q_c/T_c = 0$, so [itex]Q_c/Q_h = T_c/T_h[/tex]

From the first law: W = Qh - Qc, so

$$\eta = \frac{W}{Q_h} = \frac{Q_h - Q_c}{Q_h} = 1 - \frac{Q_c}{Q_h} = 1 - \frac{T_c}{T_h}$$

$$Q_c = Q_h\frac{T_c}{T_h}$$

AM