Specific
Heat Capacity                             18/01/18

 

Introduction:

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The aim of this experiment
was to determine the specific heat capacity of water and copper.

 

Theory:

By
definition the specific heat capacity of any substance is the energy required
to change the temperature of 1kg of the substance by 1 Celsius  The amount of energy
required depends on the substance as different substances have different
specific heat capacities, as show in the table 1 below.

Substance

c in J/gm K

c in cal/gm K or
Btu/lb F

Molar C
J/mol K

Aluminum

0.900

0.215

24.3

Bismuth

0.123

0.0294

25.7

Copper

0.386

0.0923

24.5

Brass

0.380

0.092

Gold

0.126

0.0301

25.6

Lead

0.128

0.0305

26.4

It was only less than 400 years ago when
humanity began to grasp the idea of specific heat capacity.

Joseph Black, a chemist and lecturer at the
University of Glasgow during the 18th century, was the first person
to hypothesise the idea of latent heat and specific heat capacity. He realised
that when ice is heated to melting point, there is no temperature change in the
mixture of water and ice, instead the volume of water in the mixture increased
when the temperature increased. This realisation eventually led to the theory of
latent heat, and from there to the generalization of specific heat capacity 

 

Equation 1.0 below relates the heat added
to a substance with its specific heat capacity.

 

Q =  

Where: –

–       
Q is the amount of heat
added (J)

–       
m is the mass of the
material (Kg)

–       

–       
c is the specific heat
capacity ()

 

By rearranging equation 1,0, A value for
specific heat capacity can be calculated with equation 1.1, shown below.

   c
=  
(1.1)

 

A change of temperature (will naturally result in a change of heat energy, so equation
1.1 can also be represented in the form:

 

c =  (1.2)

Where is the change of heat energy with temperature.

 

As time went on, physicists dove deeper
into thermodynamics and obviously dove deeper it specific heat. During the early
19th century a new law was hypothesised by two French physicists.
This law is the law of Dulong and Petit and was named after the scientists that
created it. This law states that the molar heat capacities for the majority of
elemental solids are around 25. This at a glance may not seem like anything out of the ordinary,
however when compared with the specific heat capacities of elemental solids a
distinct difference is noticed. This can be seen in table 1 above. Unlike the molar
specific heat capacities (C) the specific heat capacities (c) do not hover
around a set value. The only difference when calculating the molar and specific
heat capacities is that instead of using the mass of the material, the number
of moles multiplied by the molar mass per mole is used

 

The total mass of a material can be given
by the number of moles (n) multiplied by the molar mass per mole (M), Shown in
equation 3.0 below.

 

 

m = nM (3.0

When substituted into equation 1.0:

 

       
                                                     Q
= (3.1)

 

The molar head capacity (C) is equal to
Molar mass per mole (M) multiplied by the specific heat capacity(c), shown in
equation 3.2 below.

 

C = Mc

Q = (3.2)

 

The law of Dulong and Petit comes from a
deeper analysis of the difference of expressing the specific heat of an
elemental solids as energy per unit mass and as energy per mole.

The law states that the atoms in 1 mole
is the same in all elemental substances. So on the atomic level, roughly the
same amount of heat is required to increase the temperature of an elemental
solid by a specific amount

 

 Apparatus:

 

 

 

 

Diagram 1 (modelled after Figure 1, page 3 .)

 

Equipment
used:

–       
Digital
thermometer                                                                                                  –
Glass beaker

–       
Electric kettle                                                                                                                 – Copper rod

–       
Digital timer                                                                                                                    –
Thermally insulated gloves

–       
Digital scales                                                                                                                   –
Insulating foam   

 

                  

Method

The experiment was broken up into
two parts. Part 1 was to determine the specific heat capacity of water and part
2 was to determine he specific heat capacity of copper.

 

Part 1

Part 1 consisted of firstly, filling the kettle with 1 litre of tap
water and recording the initial temperature of the water. The thermometer was
then placed inside the kettle. Then the temperature changes of water during 15
second intervals were recorded with the thermometer and timer, until the water
began to boil. After this the Energy transferred to the kettle at each time
interval was calculated. A
graph was then plotted with the values of energy and temperature. Finally, the
specific heat capacity of water was calculated using the gradient of the graph
and the mass of the water.

 

Part 2

Part 2 consisted of firstly, replacing the water in the kettle with new
tap water and recording the mass of the copper rod. After this the copper rod was
suspended via the string inside the kettle. The kettle was then switched on.
While the water was boiling a beaker was filled with 200ml of cold water and
placed on top of a block of insulating foam. When the water began to boil the
copper rod was removed and placed inside the beaker, ensuring that it did not
touch any sides of the beaker. At the same time the thermometer was placed
inside the beaker, ensuring it did not touch anything but the water. The copper
rod was then removed when the temperature of the water had settled. This
temperature is the temperature which water and copper are at thermal
equilibrium.

Results

Part 1

Temperature

Time (seconds)

Energy (Joules)

20.0

0.00

0

31.1

15.0

4.14

38.8

30.0

8.28

47.6

45.0

1.24

57.7

60.0

1.66

77.7

75.0

2.07

90.0

90.0

2.48

94.1

105

2.90

98.1

120

3.31

99.2

135

3.73

100.1

150

4.14

101.1

165

4.55

Table 2

 

The energy transferred to the kettle was calculated using equation 3
below:

Energy = Power.Time

Q = P (3.0)

The power of the kettle ranged from 2520 to 3000 Joules, So an average of
this was calculated and used to calculate the Energy values.

 =     

=

= 2760 W

A
graph of the energy transferred to the kettle against the temperature was then
plotted.

 

 

 

 

Graph 1

Part 2

 

Mass of copper rod (Kg)

Initial water temperature

Equilibrium temperature

Heat energy(J)

0.436

21.3

21.9

503

 

Table 3

 

 

The value used
for the heat energy will be explained in the next segment of the report.

 

 

 

 

 

 

 

Analysis:

 

Part 1

 

Energy:

The
energy at each time interval was calculated using equation 3.0. The following
is a sample calculation of the energy at 15 seconds.

                                                            Q = P 

                                                            Q
= 2760 W. 15s

                                                            Q
= 41400J = 4.14J

The
uncertainty in Q would be the percentage uncertainty of the power and the time
added.

The
percentage error at 15 seconds for the time and the temperature are 0.6% and 0.3%
respectively. Thus, the percentage uncertainly in the energy at this time is .

 

                                    Q =  4.14J
 = =  4.14J

 

                                               

From
equation 1.1 it can be seen that the specific heat capacity if water would be the
gradient of the graph divide by the mass of the water. In this experiment, the
gradient of the graph would be the specific heat capacity of the tap water.     

                                                                        c =  

           

c =     (

 

1 litre of water was used in the
experiment and 1 litre of water is almost exactly 1 kg. The gradient of the
graph can be calculated using simple mathematics.

                                                           

                                                            Gradient =   

                                                            Gradient =         

           

 Gradient =  4190

 

The reason to which why the gradient is
the specific heat capacity is since the mass is 1kg, the value of the gradient
will not change.

                                                                                   

c =

 

c =

 

c =  4190

 

The uncertainty for the specific heat
capacity is calculated similarly to how the uncertainty in the energy was
calculated. Firstly, the average energy and temperature was calculated, shown
below.

 

                                                                      
 

                                                      

 

J                                                           

 

 

The percentage uncertainty of the energy
and temperature are  and .

                                                           

            c = 4190 4190

                                                                                                                                     

                                                                                   

 

Part 2

Equation
1 was used to calculate the specific heat capacity for the copper rod as well. The
reason for using 503J for the heat energy is because at the equilibrium temperature
of the water and copper ( 21.9 the heat energy transfer
between the copper rod and the water would be constant, so the heat energy of
the water would equal the heat energy of the copper rod and can be calculated
with equation 1.0, shown below.                                                                                       

                                                            Q(water) = 4190×0.200×0.6

                                                                               
= 502.8 J = 503J

As
Q water = Q copper at thermal equilibrium, the specific heat capacity can then
be calculated using equation 1.1, shown below.

                                                            c (copper) =

                                                                        =
1920

 

The uncertainty would be the sum of all
the individual percentage uncertainties. The uncertainties in the energy, mass
and temperature are  respectively, thus the uncertainty
in the specific heat capacity of copper is

  

 

C = 1920

           

Conclusion

 

Both experiments were successfully
fulfilled the overall aim, this being obtaining values for the specific heat
capacity of water and copper.

 

Part 1

The accepted value for the specific
heat capacity of water in  is 4.186  as the experiment used kilograms on conversion it becomes . This is very close to the value calculated during this
experiment. However, there are still a few variables that could be controlled in
a better manner. The biggest source of error is that the kettle was slightly open
when conducting the experiment. This resulted as steam being released from the
kettle as it was heated. As a result of this the mass of the tap water
decreased by a certain amount as during the course of the experiment. This would
alter the value obtained for the specific heat capacity.

 

Ideally the temperature of the water
should be measured with the kettle top closed. This could be done with a
wireless thermometer that sends the temperature values to a computer as the
water boils, or the amount of energy that was used to cause the phase change
form tap water to steam could be calculated, this having the name latent heat. This
latent energy at each time interval could then be added accordingly to each calculated
energy value.

 

Another big source of error is human
judgement. This experiment was meant to be carried out by 2 Individuals, A and
B, but due to a constraint in numbers it was only carried out by 1 individual,
C. So ideally A would look at the timer and B at the thermometer. A would notify
B every time interval. In this case, C was doing both things simultaneously,
which resulted in errors in the precision of the temperature at each time
interval.

 

Part 2

 

The
accepted specific heat capacity of copper is 0.385  when converted to kilograms
it becomes 385 . It is obvious to see that the value obtained or the specific
heat capacity of copper from this experiment is nowhere near the accepted
value. This gigantic difference has occurred either due to a multitude of
errors in the experiment or a calculation error.

 

The first cause of error is the positioning
of the equipment. Ideally when the copper rod is removed from the kettle it should
be instantly suspended in the glass beaker. Hover during the experiment the
glass beaker was positioned on at the end of the table. So during this distance
the copper rod was already being cooled. This error could be minimalized by ensuring
the beaker is positioned as close as possible to the kettle.

 

 

To conclude, the result obtained for part 1 was within the uncertainty
of the accepted value. So it can be considered as a valid experiment, however
this is not to say that the experiment was conducted as well as it could have
been. There were still a multitude of errors that

could have been dealt with in a better manner. For example, ensuring
the sufficient number of individuals are conducting the experiment.

On the contrary, the result obtained for part 2 is nowhere close to
the accepted value. It is difficult to identify any major experimental uncertainties
in the experiment as it followed the method thoroughly. So it must be a
calculation error, however after calculating the values repeatedly the values
obtained were constant. 

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