Calorimetry

Temperature

Heat is a form of energy that can be converted into other forms of energy (like
mechanical energy, electrical energy, etc.) and vice versa. We use heat for various
purposes such as cooking.
One hot day, on returning from school, Ravi touched the iron gate leading to his house.
He found it to be extremely hot. Later, he touched other things made of iron present
inside his house and found that they were not hot. Then, he touched other substances
(not made of iron) present in his house to determine whether they were hot or cold. He
listed his observations as in the table given below.
Substance Hot/ Cold
Tea Hot
Coffee Hot
Ice Cold
Ice cream Cold
Cooked rice Hot
Frozen meat Cold

Try to make a table, listing some other substances present in your house and classify
them as hot or cold. But how do you decide whether a substance is hot or
cold? Can you always tell whether a substance is hot or cold simply by touching
it? The following activity will help you understand the concept better.

Activity:

Take three containers and label them as A, B and C. Take hot water in container A, and
cold water in container C. In container B, mix hot and cold water in equal amounts.
Now, place your left hand in container A and right hand in container C for two minutes.
Then, dip both your hands in container B.
What can you say about the water present in the three containers? Note down your
observations in the table given below.
Container Hot/Cold
A
B
C

What is your observation for container B? Is the water in container B hot or cold?

When you dip your hands in container B, your left hand will tell you that the water is
cold, while your right hand will tell you that the water is hot. Thus, you will not be able to
distinguish whether the water present in container B is hot or cold.

From this activity, we can conclude that we cannot decide whether a substance is hot or
cold just by touching it. Thus, we need something more reliable than our sense of touch
to decide whether a substance is hot or cold.

Is Heat Measurable?

The measure used for detecting the degree of hotness of a substance is called
temperature.

Activity- Take water in a cup and add 2-3 drops of food colour in it.

You will notice that the food colour will spread in water. This is due to the movement
of the molecules.

Think and tell- How do you come to know that your mother is cooking something
special for you in the kitchen?
Yes, you can smell it from your room. But do you know why you are able to do so?

Every substance is made up of matter and matter is made up of atoms and molecules.
These atoms and molecules possess kinetic energy and are constantly in motion. Also,
heat is a form of energy. So, if we heat any substance, we are providing energy to it.
This added energy increases the kinetic energy of the molecules and thus, increases
the temperature of the substance.

The total kinetic energy of all the molecules in a substance is called heat and the
increase in average kinetic energy of molecules of the substance is
called temperature. The S.I. unit of heat is Joule (J) and the S.I. unit of temperature is
Kelvin (K).

Heat depends upon the mass of the substance, while the temperature does not.

Let us differentiate between heat and temperature.

Heat Temperature

The total kinetic energy of all the molecules Temperature is the measure of the
in a substance is called heat. degree of hotness of a substance.

It depends upon the speed, number, size or It does not depend upon the size or
mass and the type of the particles in the mass of the object.
substance.
The S.I. unit of heat is Joule (J). The S.I. unit of temperature is Kelvin
(K).

Relation between degree Celsius and Kelvin

T K = 273 + t °C

Hence, by adding 273 to the degree Celsius temperature we get Kelvin temperature.

t°C = T K − 273

If 273 is subtracted from Kelvin temperature, we get degree Celsius temperature.

Specific Heat and Specific Heat Capacity

Take the same amount of water in two similar beakers. Put a thermometer in each
beaker, and heat the beakers. Heat one beaker for 5 minutes and the other for 10
minutes. What do you observe?
You will observe that the water in the beaker that is heated for the longer time becomes
hotter than the other beaker. The thermometer in this beaker shows a higher
temperature. Why does this happen?

The answer is very simple—the longer the time we heat water, the hotter it becomes.
So, we can say the rise in the temperature of a body is directly proportional to the
heat energy contained in the body.

Let us do an experiment to explore more properties of heat.

As shown in the figure, take two beakers: one with 100 mL of water and the other with
200 mL of water. Now, start heating the beakers, and heat them till the temperatures in
both the beakers become the same. Do they require the same time?

You will observe that the time taken to raise the temperature of water by 30°C in the
200-mL beaker is double the time taken to raise the temperature of water (by the same
measure) in the 100-mL beaker. Perform this experiment a few more times by raising
the temperature to different levels.

Every time you will get the same result.

Hence, we can conclude that the amount of heat absorbed by a body to raise its
temperature is directly proportional to the mass of the body. The more the mass
of a body, the more is the heat required by it to raise its temperature.

Again, we take the same two beakers. Fill the beaker containing 200 mL of water with
100 mL of oil instead.
 Heat the two beakers for the same amount of time. You will observe that the
temperature of oil increases more than that of water for the same amount of heat
energy supplied. Thus, it can be concluded that water needs more heat energy than oil
to be raised to the same degree of temperature.

Hence, it can be concluded that heat energy contained in a body is directly related to
the chemical composition of the body.

Therefore, from all the experiments we can conclude that

• When the mass (m) is constant, the rise in the temperature (Δθr ) of a body is directly
proportional to the heat energy (H) supplied to it, i.e.,

H ∝Δθr(mis constant)

• When the change in temperature is constant, the heat energy (H) absorbed by an object
is directly proportional to the mass (m) of the object, i.e.,

H∝ m(Δθris constant)

• When both mass (m) and temperature change (Δθr ) are constant, the heat energy (H)
absorbed by an object depends on its chemical composition.
• Therefore, we can say that

H∝ mΔθr(Both m andΔθr are variable)

∴ H = mCΔθr

Where, C is a proportionality constant, called specific heat capacity. This depends on

the nature of the substance.
Thus,

Heat absorbed = Mass of the body × Specific heat capacity × Rise in temperature

Units of Specific heat capacity

Specific capacity (C) =

In the CGS system, the unit of heat is dyne centimeter (dyn-cm); that of mass is gram
(g), and that of temperature is °C.

Therefore, the unit of specific heat capacity in the CGS system is (dyn-cm g−1 °C−1)

In the SI system, the unit of heat is joule (J); that of mass is kilogram (kg), and that of
temperature is Kelvin (K).

Therefore, the unit of specific heat capacity in the SI system J kg−1 K−1

Water has the highest specific heat capacity of 4.2 J/g °C. In other words, every 1 g of
water will absorb 4.2 J of energy when its temperature rises by 1°C.

Measurement of Specific Heat

Measurement of specific heat of an object includes two components: mixing method

and calorimeter. In this method, a hot solid object is put in the water in a calorimeter. As
soon as the hot object is placed in water, exchange of heat occurs between the hot
object and water in the calorimeter. This exchange of heat continues till the
temperatures of the solid object, water and the calorimeter become equal.
So, we can say that

Heat lost by solid object = Heat gained by water in calorimeter + Heat gained by the
calorimeter .....(1)

The following equation will give us an idea about how to calulate the varoius
components which are present in the above equation.

Heat lost by the solid object (Q) = Mass of the solid object ×× Its specific
heat ×× Decrease in its temperature .....(2)
Heat gained by the water (Q1) = Mass of the water ×× Its specific heat ×× Increase in its
temperature .....(3)
Heat gained by the calorimeter (Q2) = Mass of the calorimeter ×× Its specific
heat ×× Increase in its temperature .....(4)

Using equation 2, 3 and 4, we can rewrite equation 1 as:

 Q = Q2 + Q1

Applications of high specific heat capacity of water:

• Climate nearby seashore is pleasant

• For fomentation, hot water bottles are used
• In car and industries, water is used as coolant
• Filling fields with water protects the crops from frost

Heat capacity or thermal capacity

The amount of heat energy required by an object to raise its temperature by 1 oC is

known as its hear capacity. Thus,

Calorimeter

Principle of Calorimetry

Calorimetry means measurement of heat. When a body at higher temperature is

brought in contact with a body at lower temperature, the heat lost by the former is equal
to the heat gained by the latter (no heat should escape to the surroundings).

Calorimeter

A device used for heat measurement is called a calorimeter.

Construction of a Calorimeter

• It consists of a metallic vessel and stirrers. They are made of copper or aluminium.

• The vessel is then kept inside a wooden jacket which contains heat-insulating materials.
• The outer wooden jacket acts as a heat shield, and reduces the heat loss from the inner
vessel.

• The outer jacket has an opening through which a mercury thermometer is inserted into
the calorimeter.

Determination of Specific Heat by a Calorimeter

• Consider a calorimeter of known water equivalent containing water.

• Note the initial temperatures of the water and the calorimeter.

• Heat the substance whose specific heat is to be determined to a particular temperature.

• Put this substance in the calorimeter, and stir the mixture.

• The substance at higher temperature will lose heat, which will in turn be gained by the
water and the calorimeter.

• Stir the mixture and note the constant temperature.

• Weigh the mixture to find the mass of the added substance.

Consider,

m1 = Mass of water

t1 = Initial temperature of the water and the calorimeter

w = Water equivalent of the calorimeter and the stirrer

m2 = Mass of the substance

s = Specific heat of the substance

t2 = Temperature of the substance

t = Common temperature of the mixture

Rise in the temperature of the water and the calorimeter = (t − t1)

Fall in the temperature of the substance = (t2 − t)

Heat gained by the water and the calorimeter = (m1 + w) (t − t1)

Heat lost by the substance = s. m2 (t2 − t)

According to calorimetry principle,

(m1 + w) (t − t1) = s.m2 (t2 − t)

Note

Rise in the temperature of a body may not be equal to the fall in the temperature of
another body.

Change of State

We know that matter exists in three different physical states − solid, liquid, and gas.
The states of matter are interchangeable i.e., a substance can be changed from its solid
state to its liquid state and vice-versa. Transitions from the liquid state to the gaseous
state and vice-versa are also possible. However, some substances directly change into
their gaseous state from their solid state and vice-versa.
Water exists in all three states (i.e., solid, liquid, and gaseous) as ice, water, and
water vapour respectively. These states are interchangeable (see the given figure).

Interchangeable nature of the three states of matter

Let us now explore how matter changes its form.

Temperature is a major factor responsible for causing a change in the various states of
matter. The changes in the states of matter with increasing or decreasing temperatures
can be shown in the form of the following figure.

Effect of temperature on the states of matter

On heating a solid substance, the kinetic energy of its constituent particles increases.
As a result, the particles start vibrating with greater speed. This extra energy helps the
particles to overcome the inter-particle force of attraction. Soon, they leave their
positions and start moving more freely. Consequently, the substance melts. The
change of solid state into liquid state is known as melting. The minimum
temperature at which a substance starts melting and becomes a liquid at
atmospheric pressure is known as its melting point.

Heating curve of ice during melting

 To obtain this curve, we plot a graph showing variation in temperature of ice at various
instant of time when a test-tube containing ice is placed on a burner. The graph is
plotted until the temperature of water (obtained after melting of ice) reaches upto to
30 oC. The reading is taken by the thermometer gently inserted into the ice such that it
does not touch the walls of the tube.

From the graph it clear that temperature of ice in the part AB remains equal to 0 oC till
the whole ice melts. The constant temperature at which the whole ice melts is known as
the melting point of ice.

Effect of pressure on melting point

• By increasing the pressure, the melting point decreases for the substances which
contract on melting . For instance ice.
• By increasing the pressure, the melting point increases of the substances which
expand on melting. For instance lead, wax etc..

Latent heat

The heat energy absorbed or liberated during the change of state of a matter and which
does not actually take part in rising or falling of the temperature of the matter is called
latent heat of the matter.

Now, this latent heat when expressed for unit mass of a matter is called the specific
latent heat and it is denoted by letter L.

Specific Latent Heat

 Hence, the specific latent heat of a state is the quantity of heat energy absorbed or
liberated by the unit mass of the substance for the change in its state at a constant
temperature. S.I. unit of specific latent heat is J kg-1.

Do you know!

It has been observed that temperature remains constant till all solid melts into liquid.
The heat supplied is used for changing a solid state into its liquid state by overcoming
the particle-particle attraction force. The solid substance absorbs heat energy without
showing any rise in temperature. This heat energy is called latent heat. The amount of
heat required to convert a unit mass of a solid into its liquid state without a
change in temperature (i.e., at its melting point) is called the latent heat of fusion.

For ice, the latent heat of fusion is 334 kJ kg-1. This means that 334 kJ of heat is
required to convert 1 kg of ice at 0ºC into 1 kg of water at 0ºC. Conversely, 334 kJ of
heat is released when 1 kg of water freezes at 0ºC to give 1 kg of ice at 0ºC.

Natural consequences of high specific latent heat of fusion of ice

• Snow on high mountains does not melt all at once

• In extremely cold conditions, water in the lakes and ponds does not freeze all at once
• Pieces of ice can cool a drink more quickly than the ice-cold water at 0 oC
• Surrounding of a frozen lake becomes extremely cold if it starts melting

If heating is continued, then the kinetic energy of liquid particles increases further. This
increases the velocity of the particles, and at a certain temperature, they obtain enough
energy to break free from the force of attraction of the other particles. At this point, the
liquid starts boiling i.e., starts changing into its gaseous state. This temperature is
known as the boiling point of the liquid.

Heating curve for water

Take some water at 20 oC (room temperature) in a flask and suspend a thermometer in
it. Now heat the flask on a burner and observe the temperature after every half an hour
till the water starts boiling and vapours are present in the flask. We will observe that the
bubbles are formed throughout the water showing that boiling occurs throughout the
volume of water.
 By plotting the graph of temperature against time, we see that the temperature of water
rises continuously in the curve AB where it is in liquid state and this is because of the
absorption of heat by water continuously. Now, at point B the boiling starts and the
temperature does not increase further which is shown by the curve BC even
thought there is also continuous absorption of heat energy. This straight line BC parallel
to time axis represents the boiling of water and the point B corresponds to boiling point
of water.

Effect of pressure on boiling point

• The boiling point of liquid increases with increase in pressure and decreases with
decrease in pressure

The latent heat of vaporisation is the amount of heat required to convert a unit mass of
liquid into its vapour state, without a change in its temperature. Latent heat of
vaporisation of water is 2,260 kJ kg-1. This means that 2,260 kJ of heat must be provided
to convert 1 kg of water at 100ºC into 1 kg of vapour at 100ºC. Conversely, 2260 kJ of
heat is released when 1 kg of vapour condenses at 100ºC to give 1 kg of water at
100ºC.

Conversely, when gas is cooled beyond its boiling point, it changes to its liquid state.
This process is called condensation. When a liquid is cooled beyond its freezing point,
it solidifies. This process is called freezing. The freezing point and boiling point of water
are 0°C and 100°C respectively.
 When a solid directly changes into its gaseous state on heating, the process is
called sublimation. The reverse process is called deposition. Sublimation can be
observed with the help of the following activity.

Have you ever heard about the term regelation?

Regelation refers to the phenomenon in which the ice converts to liquid due to applied
pressure and when the pressure is removed, then it re-converts into ice. The reason
behind this change is that the increased pressure lowers the melting point of ice below
0°C, which means that at 0°C, the ice gets converted into water. As the pressure is
removed, the melting point is restored to 0°C, which results in water getting converted
into ice again.