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The Heat Capacity of a Body
Consider the two pans shown below.  
 
The pans are of a similar type but different size.   
Each pan is filled with water.  
They are placed on heaters having the same power.  
In which pan would the water boil first? (Don't worry, it's not a trick question...)  
Obviously, the smaller one. This is easily explained:  
The temperature of a body is a measure of the average kinetic energy of the particles of the body.  
If both bodies are supplied with energy at the same rate, then the one containing the greater number of particles will require longer to change the temperature by a given amount.  
To describe this situation, we say that the bigger pan of water has a greater heat capacity then the smaller one.  
Definition:  
The heat capacity of a body is the quantity of energy needed to cause its temperature to change by 1C.  
   
Therefore, the units of heat capacity are JC-1 or JK-1 (remember that the size of the degree is the same on the Celsius and Kelvin scales).  
   
The heat capacity of a body depends on:  
1. the substances it is made of  
2. the masses of the different substances in the body.  
   
The heat capacity of a body is clearly a useful figure to know, however, imagine that you were to sit down and write a list of the heat capacities of all the bodies you could think of... 't'would be quite a long list, I think!  
   
More useful still would be a list from which the heat capacities of different bodies could be calculated.  
   
The Specific Heat Capacity of a Substance (c)  
Considering again the two pans of water.  
Suppose that the small pan holds 1kg of water and the larger one holds 3kg of water.  
It is reasonable to expect that to change the temperature of the 3kg of water, by a given amount, will require three times as much energy as to change the temperature of the 1kg of water.  
We are assuming that 1kg of water always needs the same quantity of energy to change its temperature by a given amount.  
We now define the specific heat capacity of a substance as follows:  
The specific heat capacity of a substance is the quantity of energy needed to change the temperature of 1kg of the substance by 1C.  
   
So, the units of specific heat capacity are Jkg-1C-1 or Jkg-1K-1  
   
It is perfectly reasonable to imagine a fairly exhaustive list of specific heat capacities of different substances from which we can then calculate the heat capacity of any body we might find (assuming we also know the masses of the different substances, of course).  
   
From this definition we have the following useful equation to calculate the quantity of energy, Q, needed to change the temperature, ΔT, of a given mass, m, of a known substance:  
 
   
Comparing the Specific Heat Capacities of Different Substances  
To change the temperature of a body means to change the average kinetic energy of its particles.  
The particles of different substances have different masses.  
The number of particles in 1kg of a substance obviously depends on the mass of those particles.  
This explains why different substances have different specific heat capacities.  
   
For example, the mass of an atom of iron is about twice the mass of an atom of aluminium.  
So, 1kg of aluminium must contain about twice as many atoms as 1kg of iron.  
We would therefore expect the specific heat capacity of aluminium to be about twice that of iron.  
ciron 460Jkg-1C-1
caluminium 908Jkg-1C-1
 
...I rest my case...  
NB  
The specific heat capacity of water is high compared with most other substances, cwater = (approximately) 4200Jkg-1C-1, which means that water requires lots of energy to change its temperature.  
Remember this next time you take a shower...  
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