MODULE I
ENERGY
Introduction
“Energy” is a much-used term that represents a rather abstract concept. For
instance, when we feel tired, we might say we haven’t any energy. Breakfast cereals
advertise their ability to provide energy in the morning. In sports, substitute players are
described as boosting their team’s energy. The energy crisis brought on by oil embargoes
in the 1970s is a critical component of the history of that decade, and energy remains
central to important political issues in the 21st century. This widespread use of the
concept of energy underscores its importance. It is apparent that in casual use the word
“energy” conveys many related but subtly different meanings.
Learning Outcomes
After completing this module, you should be able to:
1. Discuss the meaning of energy and its various forms;
2. Identify energy units and solve problems on energy unit conversion;
3. Discuss heat and work as forms of energy transfer
4. Explain energy transformation and solve problems on energy conservation
5. Solve problems on heat capacity and specific heat
6. Solve simple problems on calorimetry
I.1 What is energy?
Energy is usually defined as the capacity to do work. All forms of energy are
capable of doing work (that is, of exerting a force over a distance), but not all of them
are equally relevant to chemistry. The energy contained in tidal waves, for example, can
be harnessed to perform useful work, but the relationship between tidal waves and
chemistry is minimal. Chemists define work as directed energy change resulting from a
process.
I.2 What are the Forms of Energy?
Most of the energy we encounter can be placed into two broad categories:
potential energy and kinetic energy. Potential energy is energy stored in an object or
system of objects. It can be related to its position, the bonds in its chemical structure,
its potential for radioactive decay or even its shape. Consider the following examples of
potential energy associated with the relative position of an object.
a. A roller coaster gains potential energy as it is pulled up the initial slope because it
acquires a higher position relative to the ground and gravity is attracting it
downward.
b. A book resting on a desk top acquired potential energy when someone did the work
of lifting it to the desk top. The amount of potential energy of the book depends
upon the reference point chosen. The floor can be an arbitrary reference point in
this example.
Note: For each problem in gravitational potential energy, a reference point must be
specified.
An object may also have potential energy that is not connected with gravitation in
any way. For example, a compressed spring gets its energy from the push that is exerted
on it to get it into a compressed position. This energy is called elastic potential energy.
Consider the following types of potential energy.
a. Gravitational potential energy
The gravitational energy or gravitational potential energy is the energy
stored in the object because of its height above the ground within the
gravitational field.
The amount of gravitational potential energy an object has depends on mass
of the object and height of the object above ground. Objects that are at large
height above the ground have more potential energy. Similarly, objects that are at
small height above the ground have less potential energy.
Objects that have more mass have more potential energy. Similarly, objects
that have less mass have less potential energy.
Let's take for example, object C has more potential energy than object B
because object C has more mass than object B. Similarly, object A has less
potential energy than objects C because object A is present at less height.
b. Elastic potential energy
Elastic potential energy is the energy stored in an object that is stretched
or compressed. Elastic potential energy can be stored in the elastic objects such as
springs, rubber bands etc. Any spring that is stretched or compressed has stored
elastic potential energy.
Let us consider a spring that is unstretched as shown in the figure below. If
you apply force on a spring and stretch it (Shown in figure B), then the energy is
transferred to the spring. The energy that was gained by the spring is called
elastic potential energy. The amount of elastic potential energy stored in the
spring is equal to the amount of work done or energy applied to stretch the
spring. If more amount of force is applied on the spring, then more amount of
elastic potential energy is stored in the spring. Similarly, if less amount of force is
applied on the spring, then less amount of elastic potential energy is stored in the
spring.
c. Nuclear potential energy
Nuclear potential energy is the potential energy of the particles such as
protons and neutrons that are present inside the nucleus of an atom. This energy
holds protons and neutrons together to form nucleus. The nuclear particles like
protons and neutrons are bound together by the strong nuclear force.
Large amount of nuclear energy gets released in the form of heat and light
when two or more atomic nuclei get combined to form large nucleus or when one
nucleus splits into two smaller nuclei.
The process by which two or more nuclei of the atoms get combined to form
a large nucleus is called nuclear fusion. This is how sun generates its energy by
nuclear fusion of hydrogen in to helium. The process by which one nucleus split in
to two smaller nuclei is called nuclear fission.
d. Chemical potential energy
Chemical energy is a type of potential energy stored in the bonds
of atoms and molecules. The chemical energy gets released often in the form of
heat when the bonds between the atoms are broken. Chemical energy is stored
when bonds between the atoms are formed and released when bonds between the
atoms are broken.
The various examples of chemical energy include batteries, wood, coal,
gasoline, photosynthesis etc.
i. Exothermic reaction
The process by which chemical energy gets released or converted in the
form of heat energy is called exothermic reaction.
Candle flame and fire crackers are examples of exothermic reaction. The
candle flame and fire crackers release or convert chemical energy in the form of
heat and light.
Burning of wood is also an example of exothermic reaction. The chemical
energy stored in the wood gets released in the form of heat energy when we burnt
wood.
ii. Endothermic reaction
The process by which heat energy gets observed or converted in the form of
chemical energy is called endothermic reaction.
Photosynthesis is an example of endothermic reaction. Photosynthesis is the
process by which plants convert solar energy into chemical energy. Plants use the
energy from the sun to convert carbon dioxide and water into glucose and oxygen.
Evaporation of water is also an example of endothermic reaction.
Evaporation of water takes place due to absorption of heat energy.
e. Electric potential energy
Electric potential energy is the potential or stored energy that charged
particles have because of its own electric charge and its relative position to other
charged particles. Electric potential energy is also called as electrostatic potential
energy.
As we know that there is a gravitational field around the earth. Any object
placed within the gravitational field of the earth will experience a force towards
the earth.
In the similar way there exists an electric field around a charged particle.
Any charged particle that is placed in the electric field of other charged particle
will experience a force. This force may be repulsive or attractive.
Kinetic energy is the energy an object has because of its motion. It is also defined
as the amount of energy gained by an object from the state of rest to motion. The object
maintains this kinetic energy unless its speed changes. If the speed of this object
changes from the state of motion to rest, then same amount of kinetic energy is lost by
the object.
All moving objects have kinetic energy. For example, the earth revolving around the
sun, electrons orbiting the nucleus of an atom, birds flying in the sky, trains moving on
tracks, cars moving on road have kinetic energy. If the kinetic energy does not exist,
everything around us will be motionless. All objects would be unable to move. The entire
universe would be cold because heat is also a form of kinetic energy.
The kinetic energy of an object is mathematically written as
Where:
K = Kinetic energy
m = mass of an object
v = velocity of an object
The kinetic energy of an object depends on its mass and velocity. For a given
velocity, the kinetic energy of an object is directly proportional to its mass. Similarly, for
a given mass, the kinetic energy of an object is directly proportional to its velocity.
The various types of kinetic energy include:
a. Radiant energy
The energy of electromagnetic radiation or light is called radiant energy.
Radiant energy is also called as electromagnetic energy. This energy can travel
through space or medium. As we know that kinetic energy is the energy of motion.
Radiant energy is always in motion by travelling through space or medium. Hence, it
is a kind of kinetic energy.
Generally anything that has temperature gives off radiant energy. The
various examples of radiant energy include gamma rays, X-rays, ultraviolet
light, visible light (violet, indigo, blue, green, yellow, orange, and red), infrared
radiation, microwaves and radio waves. The energy transmitted to the earth from
the sun is also an example of radiant energy. This energy travels at very high speed
(299 792 458 m/s) in a straight line.
The light or radiant energy may be visible or invisible to the human eye. Just
like other forms of energy, the SI unit of radiant energy is joule.
b. Thermal energy
The internal energy of an object due to the motion and collision of atoms and
molecules is called thermal energy. Thermal energy is also called as heat energy.
Thermal energy is produced when the atoms and the molecules move faster
and collide with each other. The thermal energy of an object depends on the
kinetic energy of atoms and molecules. In hotter objects the atoms will move or
vibrate faster and has high kinetic energy, hence, they will produce more thermal
energy.
On the other hand, in colder objects, the atoms have very less kinetic
energy. Hence they will produce less thermal energy. Just like other forms of
energy, thermal energy is also measured in joules.
c. Sound energy
Sound energy is a form of energy produced due to vibration of an object.
This energy can travel through any medium by transferring energy from one
particle to another and can be heard when it reaches a person’s ear.
For example, when an object vibrates it transfers its energy to the
surrounding particles and makes them vibrate. These particles again collide with
other particles and so on. Likewise, the sound energy gets transferred from one
particle to another.
Sound energy cannot travel through a vacuum because vacuum does not
contain any particle to act as a medium. It only travels through a medium such as
water, air and solids.
d. Electrical energy
The energy of the moving electrons is called electrical energy. All the
objects in the universe are made up of small particles called atoms. Atoms are
made up of very small particles like electrons, protons and neutrons. The electrons
present in the atom always move around the nucleus of an atom. When the external
electric field or voltage is applied, the electrons present in the atom gain energy
and break the bonding with the parent atom and become a free electron. The
energy carried by this free electron is what we call as electrical energy or
electricity.
On a microscopic level, all substances and objects, from fuels to the paper, have
the same forms of energy. Any substance or object is composed of atoms and molecules.
These atoms and molecules have kinetic energy associated with their constant motion,
and they have potential energy due to the various forces they exert on one another. The
combined kinetic and potential energies of the atoms and molecules that make up an
object constitute its internal energy. Thus the roller coaster cars have three basic
forms of energy: kinetic (from their motion), potential (from their position relative to
the ground) and internal (from the molecules that compose the materials from which they
are made).
I.3 Units of Energy
The joule (J) is the SI unit of energy and is named after English physicist James
Prescott Joule (1818-1889). Then, in terms of SI base units a joule is equal to a kilogram
times meter squared divided by a second squared
.
How much is 1 J? It is enough to warm up about one-fourth of a gram of water by
1°C. It takes about 12,000 J to warm a cup of coffee from room temperature to 50°C. So
a joule is not a lot of energy. It will not be uncommon to measure energies in thousands of
joules, so the kilojoule (kJ) is a common unit of energy, with 1 kJ equal to 1,000 J.
An older—but still common—unit of energy is the calorie. The calorie (cal) was
originally defined in terms of warming up a given quantity of water. The modern definition
of calorie equates it to joules:
1 cal = 4.184 J
One area where the calorie is used is in nutrition. Energy contents of foods are
often expressed in calories. However, the calorie unit used for foods is actually the
kilocalorie (kcal). Most foods indicate this by spelling the word with a capital C—
Calorie. The figure below, “Calories on Food Labels” shows one example. So be careful
counting calories when you eat!
Figure: Calories on Food Labels
Conversion of Energy Units
Example:
The label in Figure:”Calories on Food Labels” states that the serving has 38 Cal. How many
joules is this?
Solution:
We recognize that with a capital C, the Calories unit is actually kilocalories. To determine
the number of joules, we convert first from kilocalories to calories (using the definition
of the kilo-prefix) and then from calories to joules (using the relationship between
calories and joules). So
38 kcal x
1000 𝑐𝑎𝑙
1 𝑘𝑐𝑎𝑙
x
4.184 𝐽
1 𝑐𝑎𝑙
= 160,000 J
I.4 Heat and Work: Forms of Energy Transfer
Although we can use a wide variety of classifications for types of energy, all
energy flow is either heat or work.
Heat is the flow of energy between two objects, from the warmer one to the
cooler one, because of a difference in their temperatures. Thus if we are speaking
carefully, heat is a process and not a quantity. Heat is not an entity we can pump into a
room or a cup of coffee. An object does not possess heat. In a strictly scientific sense, a
furnace does not produce heat but rather a body of warm air or hot water that has a
higher temperature than the cool air in a room.
Work is the second form of energy transfer. Work is the transfer of energy
accomplished by a force moving a mass some distance against resistance. Lifting a set of
roller coaster cars up a hill against the pull of gravity is an example of work. When we
consider macroscopic examples, we are typically viewing work in terms of mechanical
energy. Work, however, encompasses a wider range of phenomena than just mechanical
movement of macroscopic objects. The most common type of work encountered in
chemical processes is pressure-volume work (PV-work). When a gas expands, it can do
work. If an inflated balloon is released before it is tied off, it flies around as the gas
inside the balloon expands into the large volume of the room. Because the flying balloon
has mass, it is easy to see that the expanding gas is doing work on the balloon: this is
pressure-volume work.
For a more productive example of work being done by a chemical reaction, try to
look at the burning of gasoline in a car engine. Gasoline is a complex mixture of
hydrocarbons and the energy needed to propel a car is released by the combustion of
those hydrocarbons in the engine cylinders. This combustion produces carbon dioxide and
water vapor, and those gases do PV-work as they expand against the piston in the
cylinder. This PV-work is then transmitted through the drive train to move the car.
I.5 Energy Transformation and Conservation of Energy
We have introduced several ways to categorize energy. But these multiple forms of
energy are not all equally useful, so in many cases it is desirable to transform energy
from one form into another. For example, the lighting in your room is provided by
electricity, but that electricity was probably generated by the release of chemical
energy through the combustion of coal. Unless you want to try to light your room by
burning a chunk of coal, you need a way to harness the chemical energy released as the
coal burns and then convert it to electrical energy. That electrical energy must then be
conveyed to your own room, where your light bulbs convert it into radiant energy.
Now we begin to consider the laws of nature that apply when one form of energy is
converted into another. The first and foremost constraint on energy transformation is
that total energy must be conserved. If account properly for all energy conversion and
energy transfer process, the total amount of energy present must remain constant. To
account properly for all types of energy, we will need to define a number of terms quite
carefully.
System – is defined as part of the universe that is being considered or subject of
the investigation. It is a region containing energy and/or matter that is separated from
its surroundings by arbitrarily imposed walls or boundaries.
Surroundings – the remainder of the universe, even though it is not generally
necessary to consider everything else in the actual universe.
Universe – the system plus the surroundings
Boundary – the imagined wall that separates the system and the surroundings
Systems can be described in three different ways:
a. Isolated: this is a system in which no matter or energy is being exchanged with
the surroundings.
b. Closed: this is a system in which only energy is being exchanged with the
surroundings.
c. Open: this is a system in which both matter and energy is being exchanged with
the surroundings.
Examples of System
This is an open system. The system is the
pan and the surrounding is the kitchen.
This is a closed system. The system is the
pan/lid and the surrounding is the kitchen.
This is an isolated system. The system is the
thermos and the surrounding is the kitchen.
Once an appropriate choice of the system has been made, the concept of
conservation of energy immediately becomes useful. Because heat and work are the only
possible forms of energy transfer, we can attribute the overall change in energy, E, of a
system to these two components. Heat is commonly designates as q and work as w, so we
can write
∆E = q + w
The symbol ∆ (delta) is introduced here as a notation meaning “the change in.” This
symbol, is always defined as the difference between the final state and the initial state:
∆E = Efinal - Einitial
The equation includes arbitrary choices for the meaning of the signs for the
quantities of heat and work. The key is to choose consistent definitions for those signs.
Convention dictates that energy transferred into a system is given a positive sign and
energy flowing out of a system carries a negative sign. Thus when heat flows into a
system from the surroundings, the value of q is positive, and when work is done on a
system, the value of w is positive. Conversely, when heat flows out of a system or work is
done by the system on the surroundings, q and w will be negative.
By following the sign conventions for q and w, we considered the processes of heat
and work from the perspective of the system. So the value of ΔE is the change in the
internal energy of the system. This change in the internal energy of the system is exactly
offset by a change in the surroundings: ΔEsurroundings = -ΔEsystem. Thus the energy of
the universe remains constant:
ΔEuniverse = ΔEsurroundings + ΔEsystem
Example 1:
If 515 J of heat is added to a gas that does 218 J of work as a result, what is the change
in the energy of the system?
Solution:
Heat added to the system: q = +515J
Work done by the system: w = -218 J
∆E = q + w
∆E = (+515 J) + (-218 J) = +297 J
Example 2:
If 408 J of work is done on a system that releases 185 J of heat, what is the energy
change in the system?
Solution:
Work done on the system: w = +408 J
Heat released by the system: q = -185 J
∆E = q + w
∆E = (-185 J) + (+408 J) = +223 J
Practice Exercise:
1. What is the energy change for a gas that releases 38 J of heat and has 102 J of
work done on it?
2. 3000 J of heat is added to a system and 2500 J of work is done by the system.
What is the change in internal energy of the system?
3. What is the change in internal energy of a system when a total of 150 J of heat
transfer occurs out of the system and 159 J of work is done on the system?
4. Suppose there is heat transfer of 40.00 J to a system, while the system does
10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while
4.00 J of work is done on the system. What is the net change in internal energy of
the system?
5. How much heat transfer occurs from a system, if its internal energy decreased by
150 J while it was doing 30.0 J of work?
6. A system does 1.80 × 108 J of work while 7.50 × 108 J of heat transfer occurs to
the environment. What is the change in internal energy of the system assuming no
other changes (such as in temperature or by the addition of fuel)?
7. A gas in a closed container is heated, causing the lid of the container to rise. The
gas performs 3J of work to raise the lid, such that is has a final total energy
of 15J. How much heat energy was added to the system?
8. A gas in a closed container is heated with 50J of energy, causing the lid of the
container to rise. If the change in energy of the system is 30J, how much work was
done by the system?
I.6 Heat Capacity and Specific Heat
Suppose that we wish to raise the temperature of two different systems or
objects. In general, the different systems will absorb different amounts of energy based
on three main factors:
a. the amount of material,
b. the type of material, and
c. the temperature change
One way to note the importance of the amount of material is to compare the
behavior of a glass of water and an ocean. On a hot summer day at the beach, a glass of
cold water will quickly become warm, whereas the ocean water temperature does not
change noticeably over the same time. The small amount of water in the glass behaves
differently from the large amount in the ocean.
The type of material is also important. The sand at most beaches is predominantly
silicon dioxide, and it heats up much more quickly than even the shallowest water. Both
materials are exposed to similar amounts of energy from the sunlight, but they behave
differently.
Finally, the amount of energy supplied and the temperature change are also
related. On a cloudy day at the beach, the sand does not get as hot: less energy is
supplied to the sand because the clouds absorb some energy from the sun.
Furthermore, consider the demonstration below:
Blocks of five different metals – aluminum, iron, copper, zinc and lead – have the
same mass and the same cross-sectional area, but the pieces have different heights
because the metals have different densities. First the blocks are put in a pan of boiling
water to heat them all to the same temperature. Then they are transferred to a block of
paraffin. The aluminum block melts the most paraffin, iron follows as a poor second,
copper and zinc are tied for third, and lead melts the least paraffin.
This demonstration shows that different materials absorb or give off different
amounts of heat, even though the materials have the same mass and undergo the same
temperature change. Similarly, different amounts of heat are absorbed by blocks of the
same material if their mass is different and their temperature change is the same, if
their mass is the same and their temperature change is different, or if they have
different masses and undergo different temperature changes. Such objects are then
said to differ in heat capacity.
Heat Capacity
The heat capacity (C) of a substance is the amount of heat required to raise the
temperature of a given quantity of the substance by one degree Celsius. Those with a
high heat capacity warm more slowly because they absorb a greater quantity of heat;
they also cool more slowly because they give off more heat.
heat capacity =
𝑄
∆𝑇
where Q is the quantity of heat needed to produce a change in the temperature of the
body, ∆T. The unit we can use for heat capacity is J/oC.
Specific Heat
The heat capacity of an object does not describe the thermal properties of the
material of which it is made. For example, the heat capacity of 1.0 kg of copper differs
from that of 1.0 kg of aluminum, but the heat capacity of 1.0 kg of aluminum also differs
from that of 2.0 kg of aluminum. In order to obtain a quantity that is characteristic of
copper, aluminum, or any material, the heat capacities of equal masses of the materials
must be compared. This comparison yields a more useful quantity known as specific heat.
The specific heat (c) of a material is the amount of heat required to raise the
temperature of one gram of the substance by one degree Celsius. If Q represents the
quantity of heat needed to produce a temperature change, ∆T, in a quantity of material
of mass m, the specific heat, c, is given by
C =
𝑄/∆𝑇
𝑚
which when simplified yields
𝑄
C =
𝑚∆𝑇
Since 1 calorie of heat raises the temperature of 1 g of water 1 oC, the specific
heat of water is 1 cal/g.oC. in SI units the specific heat of water is 4.19 J/g.oC.
Let us solve the specific heat equation for Q.
Q = mc∆T
Thus the quantity of heat needed to produce a certain temperature change in a
body equals to product of the mass of the material, its specific heat and its temperature
change. If m is in g, c in J/g.oC, and ∆T in oC, Q will be expressed in joules.
If we chose to express the amount of material in terms of moles rather than mass,
our equation changes slightly:
Q = nCp∆T
where Cp is the molar heat capacity. The molar heat capacity is a physical property that
describes how much heat is required to raise the temperature of 1 mole of a substance
by 1 oC. As long as we know the molar mass of the substance, it should be simple to
convert between the specific heat and molar heat capacities for a few materials.
Table 1: Specific heat and molar heat capacities for some common substances.
Specific Heat, c
(J/g.K)
0.900
0.385
2.09
4.18
2.03
Substance
Al (s)
Cu (s)
H2O(s)
H2O(l)
H2O(g)
Molar Heat Capacity, Cp
(J/mol.K)
24.3
24.5
37.7
75.3
36.4
Example 1:
Heating a 24.0 g aluminum can raises its temperature by 15.0 oC. Find the value of Q for
the can.
Given:
Mass of Al = 24.0 g
Change in temperature, ∆T = 15.0 oC or 15.0 K
Solution:
Q = mc∆T
= 24.0 g x
= 324 J
0.900 𝐽
𝑔℃
x 15.0 oC
Example 2:
The molar heat capacity of liquid water is 75.3 J/mol.K. If 37.5 g of water is cooled
from 42.0 to 7.0 oC, what is Q for the water?
Given:
Molar heat capacity of liquid water, Cp = 75.3 J/mol.K
Mass of water = 37.5 g
Temperature, initial = 42.0 oC
Temperature, final = 7.0 oC
Solution:
moles of water, n =
n =
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
37.5 𝑔
18.0 𝑔/𝑚𝑜𝑙
n = 2.083 mol
∆T = Tfinal - Tinitial
= 7.0 oC - 42.0 oC
= -35.0 oC
Q = nCp∆T
= (2.083 mol) x (75.3
𝐽
𝑚𝑜𝑙.℃
x (-35.0 oC)
= -5.49 x 103 J = -5.49 kJ
I.7 Calorimetry
Calorimetry is the term used to describe the measurement of heat involved in a
chemical or physical process. Calorimetry is used to measure amounts of heat transferred
to or from a substance, Experiments are carried out in devices called calorimeters. The
heat evolved or absorbed by the system of interest is determined by measuring the
temperature change in its surroundings. Every effort is made to isolate the calorimeter
thermally, preventing heat flow between the immediate surroundings and the rest of the
universe.
General chemistry students often use simple calorimeters constructed from
polystyrene cups. These easy-to-use “coffee cup” calorimeters allow more heat exchange
with their surroundings, and therefore produce less accurate energy values.
A simple calorimeter can be constructed
from two polystyrene cups. A thermometer
and stirrer extend through the cover into
the reaction mixture.
Commercial solution calorimeters are also available. Relatively inexpensive
calorimeters often consist of two thin-walled cups that are nested in a way that
minimizes thermal contact during use, along with an insulated cover, handheld stirrer, and
simple thermometer. More expensive calorimeters used for industry and research
typically have a well-insulated, fully enclosed reaction vessel, motorized stirring
mechanism, and a more accurate temperature sensor.
Commercial solution calorimeters range from (a) simple, inexpensive models for student use
to (b) expensive, more accurate models for industry and research.
A two-step process is used to make a calorimetric measurement. The first step is
the calibration, in which a known amount of heat is generated in the apparatus. The second
step is the actual measurement, in which we determine the amount of heat absorbed or
released in the reaction of a known amount of material. The calibration can be done by
either by burning a known amount of a well-characterized material or by resistive heating,
in which a known amount of current is passed through a wire that heats due to its electrical
resistance. The heat capacity of the entire calorimeter may be obtained by measuring the
change in temperature of the surroundings resulting from a known heat input:
Known amount of heat = calorimeter constant x ΔT
or
Q = Ccalorimeter x ΔT
Once the calorimeter constant is known, the calorimeter is ready to be used for
actual measurement. Known amounts of reactants are placed into the calorimeter, initiate
the reaction, and then measure the resulting temperature change of the calorimeter. The
calorimeter constant allows us to determine the amount of heat released or absorbed in
the reaction.
Example 1:
A calorimeter is to be used to compare the energy content of some fuels. In the calibration
of the calorimeter, an electrical resistance heater supplies 100.0 J of heat and a
temperature increase of 0.850 OC is observed. Then 0.245 g of a particular fuel is burned
in this same calorimeter, and the temperature increases by 5.23 OC. Calculate the energy
density of this fuel, which is the amount of energy liberated per gram of fuel burned.
Solution:
Step 1: Calibration
Q = Ccalorimeter x ΔT
So
Ccalorimeter =
Ccalorimeter =
𝑄
∆𝑇
100.0 𝐽
0.850 ℃
Ccalorimeter = 118 J/oC
Step 2: Determination of heat evolved by fuel
Qcalorimeter = Ccalorimeter x ∆T
Qcalorimeter = 118 J/oC x 5.23 oC
Qcalorimeter = 615 J
And
Qfuel = -Qcalorimeter = -615 J
Step 3: Calculation of the energy density
Energy density = -Qfuel/m
Energy density = -(-615 J)/0.245 g
Energy density = 2510 J/g
= 2.51 kJ/g
Practice Exercise:
1. The combustion of naphthalene (C10H8), which releases 5150.1 kJ/mol, is often used to
calibrate calorimeters. A 1.05-g sample of naphthalene is burned in a calorimeter, producing
a temperature rise of 3.86 OC. Burning a 1.83-g sample of coal in the same calorimeter
causes a temperature change of 4.90 OC. What is the energy density of the coal?