How Much Energy Does a Carnot Cycle Heat Engine Expel Per Cycle?

[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

 

[Andrew Mason]

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

! 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

 

[kyle8921]

I can confirm that your calculation for the mechanical power output is correct. However, the calculation for the amount of energy expelled in each cycle by heat is incorrect. The correct equation to use is Qc = Qh - W, as you stated, but the value for Qc will not be the same as the value for Qh. Qc represents the amount of energy expelled by the heat engine to the cold reservoir, while Qh represents the amount of energy absorbed from the hot reservoir. In this case, Qc should be equal to 11,159.43 J, which is equivalent to 11.16 kJ. I would recommend double-checking your calculations to ensure accuracy. Additionally, it may be helpful to review the principles of the Carnot cycle to better understand the calculations involved.