Measuring Heat Energy
Differentiate between the Caloric Theory and the Kinetic Theory of heat as they existed in the 18th century
Caloric theory stated that fluid was existent around the atom of a solid and it will become a
liquid when the atoms are not attracted. Kinetic theory states that the motions of atoms would
generate heat.
In the early 18th century, scientists thought that heat was an invisible, fluid substance. They even
had a name for this substance – ‘caloric’. They thought that all matter possessed caloric. When
an object became warm, it was because more caloric had flowed into it. When, conversely, a
substance cooled, it was because it had lost caloric. The unit of heat was taken as the calorie.
One calorie is the quantity of heat which raises the temperature of one gram of water by one
Celsius degree.
A problem with the caloric model of heat was that the mass of this ‘caloric’ fluid could not be
detected. An object weighed before and after gaining caloric still had the same mass.
Explain how Rumford’s cannon-boring experiments provided evidence against the Caloric Theory
The American-born Benjamin Thompson, later known as Count Rumford, was puzzled that a
brass cannon tube and the chips that came from it became very hot when the hole was being
bored. The chips caused water to boil!
Rumford was acquainted with the prevailing Caloric Theory, in which heat was thought of as a
massless fluid that could enter or leave objects. Where did the caloric (heat) come from when the
cannon was being bored? It seemed that the supply of caloric was inexhaustible; as long as the
boring of the cannon continued, the brass chips (and the cannon tube) felt very hot to the touch –
i.e. gave off caloric.
Thompson decided to test a theory that maybe caloric (heat), which was already present in
substances, was being squeezed out of the brass during the boring. Thompson used equal masses
of brass chips and unbored brass at 99°C and placed them in equal amounts of water at 15°C.
Both types of brass gave the same temperature rise in the water. Hence, they both gave off the
same amount of caloric and therefore must have had the same caloric content – a contradiction of
the ‘squeezing out’ theory.
Thompson also measured the masses of objects before and after heating and found that the
masses before heating were the same as the masses after heating. Thus, if the fluid, caloric,
existed, it had no mass. To Thompson, the concept of a massless fluid was unsatisfactory. His
experiments, carried out in the late 18th century, contributed significantly to the abandonment of
the Caloric Theory.
Thompson suggested that heat was not a substance as such, but was obtained from friction. That
was why the supply of heat was almost inexhaustible; as long as the boring continued, heat was
produced. Thompson also suggested that the motion involved in the boring caused ‘particles’
within the substance to vibrate. He suggested that heat flow was related to the vibrating motion
of these particles.
Joule’s historic experiment
Joule’s calculations showed that a fixed amount of work done resulted in 1 cal of heat being
produced. (The fixed amount of work has been established as 4.186 joules, or approximately 4.2
J.) Thus 4.186 J = 1 cal
Worked example: Working off excess calories
Leon loves chocolate cake.
(a) How much work must Leon do to burn up 500 cal from a piece of chocolate cake?
(Assume that all the energy provided by the chocolate cake is converted to mechanical
work.)
(b) If Leon exerts an average horizontal force of 400 N during walking, how far must he
walk to ‘work off’ the calories?
We can explain the concept of heat energy using the Kinetic Theory of matter. According to this
theory, particles of matter are always in constant motion. Thus they possess kinetic energy. The
particles also attract and repel each other, so they also possess potential energy. The total energy
possessed by all the particles of a substance is called the internal energy of the substance (page
184). A substance of large mass would therefore tend to possess more internal energy than one
with a smaller mass.
Specific heat capacity
Unless there is a change of state, the temperature of a substance rises when it gains heat energy.
Temperature rise is therefore used in determining how it gains heat energy. Temperature rise is
therefore used in determining heat energy transfer. Experiment shows that different amounts of
heat are needed to produce the same rise in temperature in similar masses of different materials.
The specific heat capacity, c, of a substance is the number of joules of heat energy
needed to raise the temperature of 1 kg of the substance by 1 kelvin.
EH = mcΔT
The Greek symbol Δ (‘delta’) is used to mean ‘change in’. So ΔT means change in T, that is:
ΔT = final temperature – initial temperature
An iron pot and an aluminium pot of equal mass. In which pot is an egg likely to boil faster,
starting from room temperature?
In the aluminium pot. At the start of the heating, the aluminium pot will need twice as much heat
energy as the iron pot in order to achieve the same rise in temperature (since aluminium has
about twice the specific heat capacity as iron).
How many joules of heat energy are required to raise the temperature of 5.0 kg of water from
a temperature of 25°C to 35°C? (Hint: use the equation EH = mcΔθ, and the specific heat
capacity of water c, is 4200 JK-1kg-1)
Heat capacity and specific heat capacity
The heat capacity, C, of an object is the number of joules of heat energy required to
raise the temperature of the object by 1 K.
Thus
𝑬
𝑪 = ∆𝑻𝑯 or 𝑬𝑯 = CΔT
where EH is the energy supplied to the object and ΔT is the resulting temperature rise. It follows, from
equations EH = mcΔT and EH = CΔT, that for an object of mass m kg made of a substance of specific heat
capacity c, then
heat capacity of the object, C = mc
Specific latent heat of fusion
The specific latent heat of fusion, lf, of a solid is the quantity of heat required to change1 kg of
the solid into liquid without a change of temperature:
𝒍𝒇 =
𝑬𝑯
𝑱𝒌𝒈−𝟏
𝒎
𝑬𝑯 = 𝒎𝒍𝒇
Specific latent heat of vaporization
The specific latent heat of vaporisation, lv, of a liquid is the quantity of heat required to change
1kg of the liquid to 1 kg of vapour without any change in temperature, at standard pressure:
𝒍𝒗 =
𝑬𝑯
𝑱𝒌𝒈−𝟏
𝒎
𝑬𝑯 = 𝒎𝒍𝒗