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The specific heat is the amount of heat per unit mass required to raise the temperature by one
degree Celsius. The relationship between heat and temperature change is usually expressed in the
form shown below where c is the specific heat. The relationship does not apply if a phase change
is encountered, because the heat added or removed during a phase change does not change the
The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C which is higher than any
other common substance. As a result, water plays a very important role in temperature regulation.
The specific heat per gram for water is much higher than that for a metal, as described in the
water-metal example. For most purposes, it is more meaningful to compare the molar specific
heats of substances.
Transitions between solid, liquid, and gaseous phases typically involve large amounts of energy
compared to the specific heat. If heat were added at a constant rate to a mass of ice to take it
through its phase changes to liquid water and then to steam, the energies required to accomplish
the phase changes (called the latent heat of fusion and latent heat of vaporization ) would lead to
plateaus in the temperature vs time graph. The graph below presumes that the pressure is one
standard atmosphere.
Q = m LV
The energy required to change a gram of a
substance from the solid to the liquid state
without changing its temperature is
commonly called it's "heat of fusion". This
energy breaks down the solid bonds, but
leaves a significant amount of energy
associated with the intermolecular forces of
the liquid state.
Q = m LF
Energy Involved in the Phase Changes of Water
Kinetic energy: Ec = 1/2 m · v2
Potential energy: Ep = m · g · h
The data for the vaporization phase change presumes that the pressure is one standard atmosphere.
The energy required to change a gram of a liquid
into the gaseous state at the boiling point is called
the "heat of vaporization". This energy breaks
down the intermolecular attractive forces, and also
must provide the energy necessary to expand the
gas (the PV work). For an ideal gas , there is no
longer any potential energy associated with
intermolecular forces. So the internal energy is
entirely in the molecular kinetic energy.
The final energy is depicted here as being in
translational kinetic energy, which is not strictly
true. There is also some vibrational and rotational
A significant feature of the vaporization phase change of water is the large change in volume that
accompanies it. A mole of water is 18 grams, and at STP that mole would occupy 22.4 liters if
vaporized into a gas. If the change is from water to steam at 100°C, rather than 0°C, then by the
ideal gas law that volume is increased by the ratio of the absolute temperatures, 373K/273K, to
30.6 liters. Comparing that to the volume of the liquid water, the volume expands by a factor of
30600/18 = 1700 when vaporized into steam at 100°C. This is a physical fact that firefighters
know, because the 1700-fold increase in volume when water is sprayed on a fire or hot surface can
be explosive and dangerous.
Specific heat is another physical property of matter. All matter has a temperature associated with it.
The temperature of matter is a direct measure of the motion of the molecules: The greater the motion
the higher the temperature:
Motion requires energy: The more energy matter has the higher temperature it will also have.
Typicall this energy is supplied by heat. Heat loss or gain by matter is equivalent energy loss or gain.
With the observation above understood we can now ask the following question: by how much will the
temperature of an object increase or decrease by the gain or loss of heat energy? The answer is given
by the specific heat (S) of the object. The specific heat of an object is defined in the following way:
Take an object of mass m, put in x amount of heat and carefully note the temperature rise, then S is
given by
Q = C · m ·  T
In this definition mass is usually in either grams or kilograms and temperature is either in Kelvin or
degrees Celsius. Note that the specific heat is "per unit mass". Thus, the specific heat of a gallon of milk is equal
to the specific heat of a quart of milk. A related quantity is called the heat capacity (C). of an object. The relation
between Q and C is C = (mass of object) x (specific heat of object). A table of some common specific heats and
heat capacities is given below:
Some common specific heats and heat
S (J/g 0C)
C (J/0C) for 100 g
Consider the specific heat of copper, 0.385 J/g 0C. What this means is that it takes 0.385 Joules of
heat to raise 1 gram of copper 1 degree Celsius. Thus, if we take 1 gram of copper at 25 0C and add 1
Joule of heat to it, we will find that the temperature of the copper will have risen to 26 0C. We can
then ask: How much heat will it take to raise by 1 0C 2g of copper? Clearly the answer is 0.385 J for
each gram or 2x0.385 J = 0.770 J. What about a pound of copper? A simple way of dealing with
different masses of matter is to determine the heat capacity C as defined above. Note that C depends
upon the size of the object as opposed to S that does not.
We are not in position to do some calculations with S and C.
Example 1: How much energy does it take to raise the temperature of 50 g of copper by 10 0C?
Example 2: If we add 30 J of heat to 10 g of aluminum, by how much will its temperature increase?
Thus, if the initial temperature of the aluminum was 20 0C then after the heat is added the
temperature will be 28.3 0C.