Thermodynamics - please guide me through

[jumoo32]

Can someone please guide me through these problems..

(1) An inventor claims to have constructed an engine that has an efficiency of 72.0% when operated between the boiling and freezing points of water. Calculate the difference between the percentage difference between the claimed efficiency and the actual efficiency. (ans: 45.2%)


(2) An ideal refrigerator, with coefficient of performance 4.3 extracts heat from the cold chamber at the rate of 258J/cycle.
(i) How much work per cycle is required to operate the refrigerator? (ans: 60.0 J)


(ii) How much heat is added to the room environment each cycle? (ans: 318.0 J)

 

[rock.freak667]

Can someone please guide me through these problems..

(1) An inventor claims to have constructed an engine that has an efficiency of 72.0% when operated between the boiling and freezing points of water. Calculate the difference between the percentage difference between the claimed efficiency and the actual efficiency. (ans: 45.2%)

So find the maximum efficiency of the engine (meaning it uses a carnot cycle) and check the difference.

(2) An ideal refrigerator, with coefficient of performance 4.3 extracts heat from the cold chamber at the rate of 258J/cycle.
(i) How much work per cycle is required to operate the refrigerator? (ans: 60.0 J)

What is the definition of the coefficient of performance?

(ii) How much heat is added to the room environment each cycle? (ans: 318.0 J)

What is the first law of thermodynamics for a closed cycle?

 

[roam]

So find the maximum efficiency of the engine (meaning it uses a carnot cycle) and check the difference.

The efficiency of the engine is given by

e= \frac{W_{eng}}{|Q_h|}=\frac{|Q_h|-|Q_c|}{|Q_h|}= 1-\frac{|Q_c|}{|Q_h|}

We are only told that the they claim the engine has efficiency 72.0%

0.72=\frac{W_{eng}}{|Q_h|}

But we don't have any other information. So what do we need to do?

What is the definition of the coefficient of performance?

The coefficient of preformance is given by

COP=\frac{|Q_c|}{W} (cooling mode)

4.3= 258/W

W=60

What is the first law of thermodynamics for a closed cycle?

It think for cyclic process, the internal energy is equal to 0. Because Q=-W

But here Q=-W=-60

But this is wrong, the correct answer has to be 318.0 J.

 

[jrlaguna]

(A) The maximum efficiency of a thermal engine operating between Ta and Tb>Ta is 1-Ta/Tb (see Carnot efficiency at http://en.wikipedia.org/wiki/Thermal_efficiency)

(C) The internal energy is decreased at each cycle by 258J, you didn't consider that...

 

[roam]

Thank you so much, I've got it!