# Simple coefficient of performance question

## Homework Statement

Your company needs to install a cold room which will maintain a temperature of -15 degrees operating in a room where the temperature is 20 degrees. A new member of staff has considered the specifications of two manufacturers and asked you to check their figures. Explain what your decision would be.

Company A : coefficient of performance 8.5
Company B: coefficient of performance 9.7

## Homework Equations

CoP = desired output / required output

## The Attempt at a Solution

Does higher CoP simply mean that the efficiency of the cold room is higher?
I tried to use the temperature values given:
T(cold) / (T(hot)-T(cold)) = 7.37

## Answers and Replies

stockzahn
Homework Helper
Gold Member
Yes, higher COP means higher efficiency (and therefore less costs). However you calculated the COP based on the Carnot Cycle (which should perform at theoretically minimal cost):

$$COP = \frac{Q_0}{W} = \frac{Q_0}{Q_A-Q_0}=\frac{T_0\Delta S_0}{T_A\Delta S_A-T_0\Delta S_0}$$

Since in the Carnot process ##\Delta S_A =\Delta S_0## you obtain your formula

$$\frac{T_0}{T_A-T_0}=7.37$$

Since the companies offer cold rooms with higher COPs, maybe this is kind of a "trick question"...

The Carnot cycle based COP means the most efficient, right?
Since the companies offer cold rooms with higher COPs than Carnot COP, should I tell my staff not to work with these companies? (as it doesn't make sense or doesn't fit my company's demand)

stockzahn
Homework Helper
Gold Member
General answer: higher COPs are better
Specific answer: something seems to be wrong with the COPs "offered" by the companies

Joon
CWatters
Science Advisor
Homework Helper
Gold Member
I'd ask the companies how they define the COP.

Here in the UK we can buy gas heaters for houses that are 103% efficient because of the strange/hostoric way that 100% was defined.

stockzahn
Homework Helper
Gold Member
I'd ask the companies how they define the COP.

Here in the UK we can buy gas heaters for houses that are 103% efficient because of the strange/hostoric way that 100% was defined.

There is also the possibility that water or rooms are heated with the discharged heat to increase the benefit (and subsequently the COP) ...

CWatters
Science Advisor
Homework Helper
Gold Member
There is also the possibility that water or rooms are heated with the discharged heat to increase the benefit (and subsequently the COP) ...

I believe its to do with the way the input power is measured. The efficiency is output power / input power. The output power into the circulating water can be measured easily but the input power depends on the energy density of the fuel and how that's measured. When they originally measured the calorific value of the fuel they ignored the latent heat of steam lost up the exhaust. These days boilers are condensing and recover that making some appear more than 100% efficient.