# What is Calorimetry?

## What is Calorimetry?

Calorimetry is the measurement of heat exchanged.
The device used in calorimetry is a calorimeter. It is usually made of copper.
The calorimeter is lagged with an insulator and placed in a jacket with a plastic cover which has two holes for a thermometer and a stirrer.

Methods of Measuring Specific Heat Capacity
(i) Method of mixtures
(ii) Electrical Method (not on syllabus)

Describing the method of mixture

-The method of mixture involves mixing a solid with a liquid at different temperature but the specific heat capacity of either solid or liquid should be known.
-In this method a hot substance is mixed with a cold substance and then stirred. Then heat will flow from a hot substance to the cold substance until both are at the same temperature.
-If no heat is lost to the surrounding then heat lost by the hot substance = heat gained by cold substance.

Note:

Experiment to determine the specific heat capacity of a solid by method of mixture

Procedure

-Put water of mass m1 in a container of heat capacity c1
-Put calorimeter and its contents in a calorimeter jacket and record their initial temperature θ1
-Meanwhile, put the solid of mass m in boiling water in a beaker as shown in figure (i) above for some minutes. Record the boiling point θ2
-Quickly transfer the solid from boiling water to the calorimeter using a string.
-Begin to stir until the final steady temperature θ3 is obtained (the heat shield is to prevent the heating from boiling water to reach the calorimeter).
-Assume negligible heat to the surrounding.

Precautions

• The specimen must be transferred as fast as possible but with care to avoid splashing of water from calorimeter.
• The calorimeter must be insulated and placed on an insulating stand in a constant temperature bath.
• The calorimeter must be polished on its inner and outer surface to reduce heat loss by radiation.
• Stirring must be done to ensure uniform distribution of heat.

Note:

To determine the specific Heat capacity of the liquid, the same procedure above is used. However in this case, a solid of known specific heat capacity is used and Cl is made the subject of the formula.

Example 1:
A piece of metal of mass 0.5kg is heated to 100oc and then placed in 0.4kg of water at 10oc. If the final temperature of the mixture is 30oc. calculate the specific heat capacity of the metal.

Note:
Liquid take up the volume of the container when filled so when a liquid is filled in a container the volume of the container is equal to the volume of liquid filling it.

Example 2: UNEB 1993. Qn. 3(d)

A copper block of mass 250g is heated to a temperature of 1450C and then dropped into a copper calorimeter of mass

Solution:
Finding Specific Heat Capacity by Mechanical method

-Lead shots of measured temperature 𝜃1 and mass “m” are placed in a tube as shown above. When the tube is inverted, they fall through distance “h”. so potential energy of the lead shots is mgh.
-This energy becomes kinetic energy which in turn becomes internal molecular energy when the lead shots are brought to rest. The internal molecular energy is heat energy which rises the temperature of lead shot from

Heat energy gained by the lead shots is equal to the potential energy lost by lead shot.

When the tube is inverted N times then the total potential energy is calculated as Nmgh so that heat gained is equal to potential energy lost.

Where N is the number of time the tube is inverted. g is acceleration due to gravity and h is the distance through which the lead shots have fallen.

The distance “h” is the same as the length of the tube. This method is more advantageous than the method of mixtures because here the mass of substance is not required.

Example:
A tube length 10cm contains leads shots. If the tube is inverted 1000 times such that the temperature of the shots changes from 40oc to 100oc. calculate the specific heat capacity of the lead shots.

Example:
A tank holding 60kg is heated by 3KW electric immersion. If the specific heat capacity is 4200J/kgk. Calculate the time taken for the temperature to rise from 10oc to 60oc.

Solution:

Latent Heat (Hidden heat)

(a) Latent Heat
Latent heat is the quantity of heat absorbed or released at constant temperature by a substance during change of state.
Specific latent heat is the heat required to change one kilogram of substance from one state of matter to another without changing its temperature.

When a substance changes state from solid to liquid or liquid to solid liquid to gas the temperature remains constant although heat is supplied.

This can be explained by the kinetic theory.
When a solid is changing in state there is no temperature change because the supplied heat energy is being used by molecules to break away the intermolecular force holding them in one state.
Latent heat therefore is the heat which causes no change in temperature but changes the state, say solid to liquid, liquid to solid or liquid to gas.

b) Types of latent Heats
(i) Latent heat of fusion; 𝐋𝐯
Latent heat of fusion is the quantity of heat required to change the state of a substance from solid to liquid at constant temperature.
Specific Latent heat of fusion is the quantity of heat required to change the state of a 1kg mass of substance from solid to liquid at constant temperature.
The S.I unit is a 𝐉𝐤𝐠−𝟏

Experiment to determine the specific latent heat of fusion by method of mixtures.

-Pour pure hot water of known mass, 𝐦𝐇𝐰and specific heat capacity 𝐂𝐰 in a well lagged calorimeter of mass, 𝐦𝐜and specific heat capacity 𝐂𝐜.
-Record the initial temperature of,θ1of hot water.
-Place small pieces of pure melting ice at 00C into the calorimeter and stir the mixture gently until all the ice melts.

• Read and record the final temperature of,θ2of the mixture in the calorimeter.
-Re weigh the calorimeter and its content to determine the mass of melted ice 𝒎𝒊from the formula;

Experiment to determine the specific latent heat of fusion by Electrical method.

Procedures:

a) Placing heater;
An electric heater of known power “p” is placed in filter funnel.

b) Packing small pieces of ice
Small pieces of ice are packed around the electric heater.

c) Switching on and timing;
The heater is switched on for a known time “t” and mass “m” of water collected in the beaker is weighed and determined from the formula:

The specific latent heat of fusion of ice,𝐋𝐟 is calculated from the formula; 𝐏𝐭=𝐦𝐋𝐟

Assumption;
No heat is absorbed from the surrounding.
All heat supplied by the heater has been absorbed by the ice only.

Significance of high value of specific latent heat of fusion

Ice is often used as a cooling agent e.g. ice cubes are added to juice to keep it cold.

(ii) Latent heat of vapourisation
Latent heat of vapourisation is the quantity of heat required to change the state of a substance from liquid state to gas at constant temperature.

Specific Latent heat of fusion is the quantity of heat required to change the state of a 1kg mass of substance from liquid state to a gas at constant temperature.
The S.I unit is a 𝐉𝐤𝐠−𝟏

Importance of the very high value of specific latent heat of vapourization of steam
[ 𝐋𝐯=𝟐,𝟐𝟔𝟎,𝟎𝟎𝟎𝐉𝐤𝐠−𝟏]

𝟐,𝟐𝟔𝟎,𝟎𝟎𝟎𝐉𝐤𝐠−𝟏]
Because of high value, steam is used as a heating agent e.g. In cookers (cooking)
Can be used for sterilizing medical tools e.g. blades, forceps, e.t.c.

Experiment to determine the specific latent heat of vapourization by method of mixtures.

-Pour pure cold water of known mass, 𝐦𝐜𝐰and specific heat capacity 𝐂𝐰 in a well lagged calorimeter of mass, 𝐦𝐜and specific heat capacity 𝐂𝐜.
-Record the initial temperature of,θ1of cold water.
-Pass steam from boiling pure water at 1000C into cold water in the calorimeter for some time and stir the mixture gently until all the temperatures are steady.

• Read and record the final temperature of,θ2of the mixture in the calorimeter.
-Re weigh the calorimeter and its content to determine the mass of melted ice 𝒎𝒔from the formula;

Heat lost by hot steam and condensed water from steam is equal to heat gained by cold water and calorimeter

Determination of specific latent heat of vaporization of steam by electrical method

Procedures:

a)Weigh the mass of water and the beaker and record it as m1.
b) Placing heater;
An electric heater of known power “p” is placed in the water in a can placed on top of a beam balance.
c) Switching on and timing;
The heater is switched on for a known time “t” and Weigh the mass of water and the beaker again and record it as m2.
d) Finding mass of steam
The mass “m” of steam escaped is determined from the formula:

Conclusion:
The specific latent heat of vapourisation of steam 𝐋𝐯 is calculated from the formula;

Latent heat and kinetic theory
(a) Latent heat of fusion.

During change of state from solid to liquid (melting) at constant temperature, the heat supplied weakens the intermolecular forces of attraction, the molecular spacing increase, changing from static molecules of solid to fast moving molecules in liquid state.
The average K.E of molecules remaining constant because melting takes place at constant temperature.

(b) Latent heat of vaporization;
During change of state from liquid to vapour, (Boiling) at constant temperature, the heat supplied weakens the intermolecular forces of attraction, the molecular spacing increase, so that they gain freedom to move about independently.
As a result, the heat supplied is used to overcome these forces resulting in gain molecular potential energy but not their kinetic energy and also the work to expand against atmospheric pressure.

Why specific latent heat of vaporization of a substance is always greater than specific latent heat of fusion for the same substance.

Specific latent heat of vaporization is always greater than Lf because for molecules of a liquid to escape, they require a lot of heat which increases the K.E in order to overcome the intermolecular forces of attraction.
While for latent heat of fusion very low amount of heat is required to weaken the intermolecular forces of attraction.

Effect of latent heat of vaporization
When steam at 100oc condenses on your body, it produces more serious burn than one would have from an equal mass of water at 100oc because when steam condenses latent heat is given out.

How to apply the formula in calculations
The following should be noted;

1. When applying the heat formula for change of state from either solid to liquid or liquid to solid the value of specific latent heat of fusion should be used.
2. The substance must either be at the melting point temperature for solid to liquid or at freezing point temperature for liquid to solid.

a) For a solid at melting point changing to liquid at freezing point.
Example I: How much heat is required to melt 10g of ice at 0oc given specific latent heat of fusion is 3.36 x 105 J/Kg.

Solution

b) When the solid is not at the melting point changing to a liquid at freezing point
In this case heat energy for changing the temperature to melting point is required. The heat for change the solid to liquid is applied, so heat energy required = Heat for change of temperature to melting point.+ Heat for change of state

Example 2:
How much heat is required to change 10g mass of ice at – 10oc to water at 0oc. Given that the specific heat capacity of ice is 2100J/KgK. and the special latent fusion of ice is 3.36 x 105 J/Kg.

Solution

Heat for change of temp at melting point to a given temperature.