Calculating efficiency of a boiler

In summary, the electric boiler is inefficient and is using more power than is required to heat the water.
  • #1
davet101
2
0
Hi, I've been attempting this problem all week now and I can't seem to even begin to obtain an answer which is highly frustrating, so here's the problem:

An electric boiler is required to raise the temperature of 90 litres of water per hour by 35oC.

If the input required to affect this change is 4.3235kW, calculate the efficiency of the boiler.

Find the cost of operating the boiler for a period of 5 hours if electrical energy costs 13p/kWhr.


Homework Equations



I have some equations which could be useful, but I can't seem to apply them to this particular problem, the equations I have looked at are:

n (efficiency) = Useful energy output/Total energy input

and

Maximum theoretical thermal efficiency = (Temperature Hot - Temperature Cold)/Temperature Hot


Unfortunately I have no attempted solution to show as I haven't been able to get anywhere with this. I do know however that the temperature will have to be converted into Kelvin (the easy bit).

I have thought about considering the Specific Heat Capacity of water but don't know how it would apply to this problem.

Any help is greatly appriciated.
 
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  • #2
The specific heat capacity of water tells you how much energy input (in the form of heat transfer) is *required* in order to raise the temperature of a unit mass of water by a unit (e.g. by 1 degree celsius).

Knowing that, and knowing how much water you have to heat by what temperature in a time of one hour, can you see that it is possible to deduce how much energy per unit time (i.e. power) is going into the water to heat it? Can you also see that comparing this to how much energy per unit time (power) is being used by the boiler will give you the efficiency. If the former power level is less than the latter, obviously some power is being lost due to inefficiency.
 
  • #3
Thanks for that, think it's done the job. My solution to the problem is now this:

From my notes the s.h.c of water is: 4200J/Kg K

Using the formula: Q = mc(t1-t2)

In this case m=90 (as far as i know 1 litre of water has a mass of 1kg)
c=4200
and t1-t2=35oC (the change in temperature)

so...

Q = 90 x 4200 x 35 = 13,230,000 J

and 1W = 1J/s

So for the amount of energy used per hour, the amount of seconds in one hour must be obtained, which is 3600 seconds.

so, 13,230,000/3600 = 3675W/hr

Now the effiency can be calculated, using n (efficiency) = useful energy output/Total energy input

so, n (efficiency) = 3675/4323.5 = 0.8500057...

Multiply by 100 to get percentage efficiency: 0.8500057... x 100 = 85.00057%

Does this look about right?
 
  • #4
Yeah, it does. Nice work!
 

What is the efficiency of a boiler and why is it important?

The efficiency of a boiler refers to the percentage of energy input that is converted into useful heat output. It is an important measure of how well the boiler is performing and can impact energy costs and environmental impact.

How is the efficiency of a boiler calculated?

The efficiency of a boiler is calculated by dividing the heat output by the fuel energy input. The heat output can be determined by measuring the steam flow and temperature, while the fuel energy input can be measured by the amount of fuel consumed or its calorific value.

What are the factors that can affect the efficiency of a boiler?

The efficiency of a boiler can be affected by various factors, such as the type and quality of fuel used, the design and size of the boiler, the operating conditions (e.g. temperature and pressure), and the maintenance and upkeep of the boiler.

What is considered a good efficiency for a boiler?

A good efficiency for a boiler can vary depending on the type and size of the boiler, but generally, an efficiency of 80% or above is considered good. However, the efficiency of a boiler should always be compared to the manufacturer's stated efficiency to determine its performance.

How can the efficiency of a boiler be improved?

The efficiency of a boiler can be improved by regular maintenance and tune-ups, using high-quality and properly sized fuel, optimizing operating conditions, and upgrading to a more efficient boiler model. It is also important to regularly monitor and track the efficiency to identify any potential areas for improvement.

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