# Thermodynamics - please guide me through

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
Homework Helper
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?

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.

(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...

Thank you so much, I've got it!