Building Design and Construction Handbook - Merritt - Ventech!

13.10 SECTION THIRTEEN
Hence, this first law of thermodynamics can be expressed mathematically by the
following equation:
W � JQ (13.4)
where W � work, ft-lb
J � Joule’s constant � mechanical equivalent of heat
Q � heat, Btu, generated by the work
Experiments have shown that the mechanical equivalent of heat, known as Joule’s
constant, is equivalent to 778 ft-lb/Btu. The first law is also known as the law of
conservation of energy.
The second law of thermodynamics states that it is impossible for any machine
to transfer heat from a substance to another substance at a higher temperature (if
the machine is unaided by an external agency). This law can be interpreted to imply
that the available supply of energy for doing work in our universe is constantly
decreasing. It also implies that any effort to devise a machine to convert a specific
quantity of heat into an equivalent amount of work is futile.
Entropy is the ratio of the heat added to a substance to the absolute temperature
at which the heat is added.
where S � entropy
dQ � differential of heat (very small change)
T a � absolute temperature
dQ
S � (13.5)
T a
The second law of thermodynamics can be expressed mathematically with the
use of the entropy concept.
Suppose an engine, which will convert heat into useful mechanical work, receives
heat Q 1 from a heat source at temperature T 1 and delivers heat Q 2 at a
temperature T 2 to a heat sink after performing work. By the first law of thermodynamics,
the law of conservation of energy, Q 2 is less than Q 1 by the amount of
work performed. And by the second law of thermodynamics, T 2 is less than T 1.
The universe at the start of the process loses entropy �S 1 � Q 1/T 1 and at the end
of the process gains entropy �S 2 � Q 2/T 2. Hence, the net change in the entropy of
the universe because of this process will be �S 2 � �S 1.
Furthermore, this law requires that this net change must always be greater than
zero and that the entropy increase is and must always be an irreversible thermodynamic
process.
�S � �S � 0 (13.6)
2 1
Because of the irreversibility of the process, the energy that has become available
for performing work is
13.2.5 Absolute Temperature
Q � T (�S � �S ) (13.7)
u 2 2 1
The definition of entropy given above involves the concept of absolute temperature
measured on a ratio scale. The unit of absolute temperature is measured in degrees