Heat and Thermodynamics
Heat Engine
A "heat engine" is a machine which converts internal energy (from a high temperature body) into some other form of energy.
The conversion of energy from some other form of anergy to internal energy of a sunstance can be done with 100% efficiency of conversion. For example, 100 J of electrical energy will be converted to 100 J internal energy by a resitstor. Conversion of energy from internal energy to some other from cannot be done with the same efficiency.
One statement of second law of thermodynamics "no heat engine, operating in a continuous cycle, can do work without transferring some internal energy from a hot body to a cold body."
The hot body is called the heat source and the cold body (often the surroundings) is called the heat sink.
Heat engines are often represented by diagrams like the figure given.
During each cycle:
W is the net work done by the engine.
is the energy taken from the (hot) source.
is the energy given to the (cold) sink.
The thermodynamic efficiency (or just efficiency), of the engine is defined to be
= 
This fraction is usually multiplied by 100 to give a % so, if the net work done is only equal to half of the energy taken from the source, the engine has an efficiency of 
= 50%.
W = 
_ 
so, 
= 
= 1 
.
Experiments show that increases as the difference between 
and 
increases. It has been shown that the theoretical maximum efficiency of a heat engine is given by
= 1 _
For an engine operating at maximum efficiency
= 
or, 
= 
In other words, for an engine operating at the theoretical maximum efficiency, the quantity 
for the source will be equal in magnitude to the same quantity for the sink.
Entropy
Entropy is defined as 
= 
, where 
represents the quantity of energy entering or leaving the body and T represents the absolute (or Kelvin or thermodynamic) temperature at which the energy transfer takes place.
At 0 K (absolute zero) the atoms of a substance are stationary. They form a well ordered arrangement. When energy flows into a body its atoms vibrate, they become a less well ordered arrangement.
Energy entering a body increases disorder
Energy leaving a body decreases disorder
Boltzmann showed that changes in entropy of a body can be considered as a direct measure of changes in the disorder of the arrangement of the particles.
When a hot body is brought into thermal contact with a cold body for a short time:
- Each body will experience a change in the entropy of its particles.
- The hot body experience a decrease in entropy (a negative change) of magnitude
= 
.
(iii) The cold body experiences an increase in entropy (a positive change) of magnitude
= 
.
(iv) The net change in entropy
= 
+ 
.
An alternative statement for the second law of thermodynamics-The effect of naturally occurring processes is always to increase the total entropy (or disorder) of the universe.