Thermal Energy

The internal energy or thermal energy of a substance is determined by the movement of the molecules and the potential energy of the arrangement of molecules.

Temperature is the measure of the
average kinetic energy of the

Heat energy is the energy transferred
from a warmer substance to a
colder one by the collisions of
The unit for all energy is the joule. However, sometimes the calorie is used for heat. The calorie is defined as the amount of heat needed to raise 1 g of a substance 1 degree Celsius.
1 cal = 4.18 joules or 1kcal = 4180 J
To convert calories to joules
multiply the calories by
To convert joules to calories
divide by 4.18.

Temperature is measured by the
changes it causes in matter like
expansion. A thermometer is one of
the instruments used. A
thermocouple is another.

There are two temperature scales
used in the SI.
1. Celsius scales sets zero at the
freezing point of water and 100 at

2. Kelvin scale (sometimes called
the absolute scale) sets 0 at
absolute zero the point at which a
substance has no kinetic energy.
The freezing point of water is 273 on
this scale and boiling is 373.

The Fahrenheit scale is the scale
commonly used in the English
system. It sets freezing at 32 and
boiling at 212.

Heat Transfer

1. Conduction - heat transferred by
Example: metal spoon gets hot in a
pot of boiling water

2. Convection - heat transferred by
the movement of fluids (gases and
Example: hot air rises in a room.

3. Radiation - heat transferred by
waves (infrared) no material is
Example: heat reaches earth from
the sun.

Heat transfer will stop when thermal equilibrium is reached, that is the rate at which energy flows out of a substance equals the rate that energy flows into the substance.

Calculating Heat


Specific heat is the amount of heat
needed to raise the temperature of
1kg of a substance 1 degree.

Q = mcDT

m - is mass in kg
c - is the specific heat of the material
DT - change in temperature


Law of Heat Exchange

According to the law of conservation of energy, energy cannot be created or destroyed. This is also true of heat energy.

If a substance gets hotter something else must get colder.

heatlost = heatgained

mcDTlost = mcDTgained


For example: 200 g of water at 80 degreesC is mixed with 200 g of water at 10 degree C. What is the final temperature?

The 80 degree water will lose heat and the 10 degree water will gain heat. They will eventually come to thermal equilibrium and be at the same temperature.

(.2kg)(4180 J/kg*C)(80-Tf) = (.2kg)(4180 J/kg*C)(Tf - 20)

66,880 J -(836 J/C) Tf = (836J/C) Tf -16,720J

(1672J/C) Tf = 83600 J

Tf = 50 C

Phase Changes

Matter occurs commonly in 3 phases. When a phase change occurs heat is needed to rearrange the molecules. This heat does not change the kinetic energy
so the temperature does not change.
during a phase change.

The boiling point is the temperature
at which vaporization/condensation
The heat needed to vaporize or condense a substance is called the Heat of Vaporization.
The heat of vaporization is the
amount of heat need to vaporize or
condense 1 g or kg of a substance.
The heat of vaporization of water is
540cal/g or 2.26 x 10^6 J/kg. This means for every g of water that evaporates 540 cal of heat must be absorbed.
For every g of water vapor that
condenses to liquid water 540 cal
must be lost.

To calculate the heat needed to make
this phase change Use the following
equation: Q = mH

Q= energy
m = mass
V = heat of vaporization

Example: How much heat would it take to change 3 kg of water at 100 degrees C to steam?

Q = (3 kg)(2.26 x 10^6 J/kg)

Q = 6.78 x 10^6 J

The freezing point of a substance is
the temperature at which freezing/
melting occurs.
The amount of heat that must be
removed for a liquid to freeze or
added for a solid to melt is called the
Heat of Fusion.
The Heat of Fusion is the amount
of heat necessary to freeze/melt 1 g or kg
of a substance.
The heat of fusion of water is 80
cal/g or 3.34 x 10^5 J/kg

To calculate the amount of heat
involved in freezing or melting use
the following equation:

Q = mH

Q = heat energy
m = mass
F = heat of fusion

Example: How much heat would it take to melt .5 kg of ice at 0 degrees C?

Q = (.5 kg)( 3.34 x 10^5 J/kg)

Q = 1.67 x 10^5 J


Determining Total Heat

Before a substance can change phase it must reach its freezing/melting or boiling/condensing point. The heat needed to reach this point is determined by the temperature change equation:

Q = mcDT

(It should be noted that the specific heat (c) of a substance as a liquid or a gas is not the same as the solid. Therefore after a phase change a different specific heat must be used!Check the table.)

The latent heat to change phase is next calculated by using the equation for the phase change:

Q = mHf or Q = mHv

The heats are then added together to find the total heat.

Example how much heat will it take to turn 2 kg of water at 30 degrees celsius to steam?

First you must calculate how much heat it will take to change the temperature of the water from 30 to 100 degrees C and then how much heat it will take to change the water to steam.

Q = mcDTH2O + mHf

Q = (2kg) (4180 J/kg*C)(100-30 C)

+ (2kg)(2.26 x 10^6 J/kg)

Q = 585,200 J + 4,520,000 J

Q = 5,110,000 J


Laws of Thermodynamics


Thermal energy can be increased either by adding heat or by doing work ona system.

DQ = Work + Additional Heat


1ST Law of Thermodynamics -the total increase in the thermal energy of a system is the sume of the work done on it and the heat added to it,

This is just a restatment to the Law of Conservation of Energy.


The converison of mechanical energy to thermal energy (rubbing your hands together) is easy. The reverse process, conversion of thermal to mechanical energy is more difficult.

Heat engines are devices able to convert thermal energy to mechanical.

Example: A 4.2 g lead bullet moving at 275 m/s steel plate and stops. If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change?


KE = 1/2 mv^2

Q = mcDT


If all the kinetic energy is converted then: KE = Q


1/2mv^2 = mcDT

1/2(.0042kg)(275m/s)^2 = (.0042kg)(130J/kg-C)DT

75625 = 130DT

290 degrees = DT

2ND Law of Thermodynamics -natural processes go in a direction that increases the total entropy of the universe

Entropy is defined as disorder.



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