Core Physics Topic 4 - Heating Buildings

It costs a lot to heat a house.  And it is getting more expensive year-on-year.  Here is a typical house, and we will look at the various measures that we can take to reduce heat loss, and reduce fuel bills.



Even in an old house it is possible to improve the insulation.


Question 1

How might you improve the insulation on this old house without spending a fortune?




Building engineers use the U-value to measure the effectiveness of the insulation.  The U-value measures how well a building component like a wall, a double glazed window, or a door keeps the heat inside a building.  In hot countries, it indicates how well it keeps heat out; people want their houses to be cool.  The lower the U-value, the better the insulation. 


The U-value is defined as:

the energy in watts that flows through a building component of 1 square metre across a temperature difference of 1 Kelvin.


A temperature difference of 1 Kelvin is the same as a temperature difference of 1 degree Celsius.


The units for U-values are Watts per square metre per Kelvin (W m-2 K-1).


Consider this wall which has a high U-value.


This wall will let a lot of heat out.  This will give rise to a number of problems:

Poor people often have poorly built nineteen-sixties houses are difficult to heat, and they cannot afford the heating either.  The cold houses suffer badly from condensation, leading to many health problems.


The U-value can be lowered by adding a layer of insulation, covered with plasterboard.  Builders call this dry-lining.  It is effective and not very expensive to install.  However it does reduce the size of the room.


Using building components with low U-values (i.e. good) has these advantages:

The house built with low U-values uses a lot less energy and the energy bills are less.


Components with low U-values increase the  temperature on the inside.   This prevents growth of mould and fungus, and improve the health of the people living there.


A good U-value for a wall is 0.2 W m-2 K-1 and for a window, it's 1 W m-2 K-1.


Question 2

Look at this bar-chart that shows the U-values of some windows.


a. Which type of window loses least heat? 

b. Which is better for window frames wood or metal? 

c. What three things does the rate of heat loss depend on? 



The two pictures show thermograms (thermal pictures) taken by equipment made by the German company InfraTec.




They show the difference in the heat flow from a building before (left) and after (right) renovation.


Question 3

Explain the differences in the heat flows from the building before and after the renovation.

Suggest some ways in which this has been done.




Heating houses

The physics of heating homes depends on the heat transfer processes of conduction, convection, and radiation.


The earliest form of heating was the open fire, which passed most heat by radiation.  Convection took the smoke up the chimney, and a good amount of the warm air from the room.  Open fires are very inefficient.  Having the fire enclosed in a stove is more efficient.  The room would be heated by convection.  The hot stove would also pass heat by radiation.  Stoves have the advantage that:

The disadvantages are:

In modern houses it is possible to have permanently mounted gas or electric heater in each room.  The gas heaters have a flue (exhaust) that goes through the wall of the house.  These have the attraction that you only have to pay for heating one room, rather than every room in the house.



Question 4

Answer the matching question for the diagram above. (AQA past question)



Central heating driven by a boiler was introduced in the late nineteenth century.  The heated water circulates by convection to radiators in the rooms.  In modern installations, the convection is assisted by a pump which assists the convection.  Modern central heating systems are powered by gas, oil, or (more rarely) solid fuel.


Central heating systems have two functions:

  1. to heat the rooms;

  2. to heat the hot water for sinks, wash-basins, and the bath.

Many modern houses have no hot-water cylinder.  Instead the combi-boiler heats the water instantly, ready for use. 


Modern boilers extract more heat by condensing water from the flue-gases.  The condensed water is drained away by an external pipe.  Unfortunately, in many houses, the drain-pipe froze in the very cold winters of 2009 and 2010, making the boilers shut down.



Electric central heating works by using night-storage heaters.


These work by electrical elements heating up large storage bricks.  The elements are switched on during the night when electricity is cheap.  They store the energy as internal energy, releasing it as heat during the day.


The advantages are:

The disadvantage is that:

Many rural areas have no gas supply.  Therefore the choice is between oil and electric central heating.



Domestic heating bills are getting more and more expensive.  The prices go up like a rocket when fuel is expensive, but drift down on a parachute when the fuel is cheap.  The Government defines fuel poverty as being when a household spends more than 10 % of its annual income on fuel.


Ask your parents about your family fuel bills.


Solar Energy

Many people are now putting solar panels on their houses.  These can be used to:

Picture by Pujanak, Wikimedia Commons


The picture shows solar panels to generate electricity.  These are called photovoltaic panels.  In the Summer the Sun delivers energy (its intensity) at a rate of 550 watts per square metre.  However solar panels are not very efficient.  They convert no more than about 10 % of that energy into electricity or heat for heating water.  That means that a 1 m2 solar panel can capture about 55 watts.  However there are some other things to think about:

You can have arrays of batteries to store the energy.


Question 5

Look at the panels on the house in the picture.  Each panel is 0.9 m 1.35 m.


(a) What is the area of each panel?

(b) The intensity from the sun is 550 W m-2.  What power falls on each panel?

(c) Only 10 % of the energy on each panel is actually turned into electricity.  What is the power of each panel?

(d) How many panels are there altogether?

(e) What is is the total power that these panels can give out?




Photovoltaic panels are very expensive.  The array in this picture would cost in the order of 15 000 (18 000).  Government subsidies have been available for people to pay for these arrays, and for the excess electricity these produce.  However these have recently been cut.


A householder may earn about 500 a year from the electricity sold to the national grid.  We can work out the time taken for the householder to get his or her money back.  This is called the payback time.


Payback time = cost money saved each year


Question 6

A solar panel array costs 15 000 to install.  It earns the householder 500 a year.


How long is the payback time?




Heating Water

A solar panel can be made to heat water.  You can make one yourself from recycled materials.  An old central heating radiator painted black and mounted in a glass-fronted box will make a reasonable solar heater.  The the hot water from the solar heater is pumped to the hot water cylinder.  However it takes a lot of energy to heat water.


Water can hold a lot of energy because it has a high specific heat capacity.  Specific heat is defined as:


the amount of energy to raise 1 kg of water through a temperature difference of 1 degree Celsius.


The formula is


Energy (J) = mass (kg) specific heat (J kg-1 K-1) temperature change (K)


You will notice from the formula that the temperature change is in Kelvin (K).  It can also be written in oC as a temperature change of 1 K = temperature change of 1 oC.


1 K is not written 1 oK.


In Physics code, the formula is written:


E = mcDq


(E - energy in J; m - mass in kg; c - specific heat capacity in J kg-1 K-1; Dq - temperature change in K or oC)


The strange looking symbols are:

Worked example

How much energy is needed to raise the temperature of 1.5 kg of water from 20 oC to 100 oC?  Specific heat of water is 4200 J kg-1 K-1.


Temperature change = 100 - 20 = 80 K

 Energy = 1.5 kg 4200 J kg-1 K-1 80 K = 504 000 J


Another useful form of the formula is:


This enables us to work out the specific heat capacity.


Question 7

2000 J of energy are supplied to a 0.6 kg block of material.  The temperature rises by 12 oC.  What is the specific heat capacity of this material?



Water has a very high specific heat capacity.  This enables it to carry a lot of energy and is useful in:

Some substances have higher specific heat capacities than water:



Specific Heat Capacity (J kg-1 K-1)






14 300


No, that last figure is NOT a typo.  This makes hydrogen a very useful coolant in a power station generator.