Page 19 - 4461

All right, let’s go to another aspect of the heat. The second
way of calculation quantity of the heat connects with
conception entropy. Fig 1.9 shows a graph obtained by
plotting T against S. It is called a T–S diagram or heat
diagram.
The initial state of the gas is represented by the point 1
and its final state – by the point 2. In fig 1.9, the gas changes
from state 1 to state 2 along path 1-2. The heat absorbed in
this process is equal to area under curve 1- 2.
Fig.1.9 - T-S diagram

S 2
Q  dQ  Tds  area 12S 1S 2 (1.38)


S 1

1.6.6 Heat and work are a path function
There are many different ways in which the system can be taken from the initial
state 1 to the final state 2. For example (fig.1.8 ), the pressure may be kept constant
from 1 to 3 and then kept constant from 3 to 2. Then the work done by the expanding
gas is equal to the area under line 1–3. Another possibility is the path 1–4–2, which case
the work done by the gas is the area under the line 4–2. The curve from 1 to 2 is another
possible path in which the work done by the gas is still different from the previous two
paths. We can see, therefore that the work done by system depends not only on the
initial and final states but also on the intermediate state, that is, on the path of process.
A similar result follows if we calculate the flow of heat during the process. The heat
flowing into the system depends on the path of the process. Each path gives a different
result for the heat into the system. Both heat and work “depend on the path”.

1.7 The First Law of Thermodynamics
Thermodynamics is characterized by a great number and diversity of applications of
its few basic principles. One of these basic principles, the first law of thermodynamics,
is introduced in this chapter, and several examples of its use are presented. It is shown
that the conservation of energy principle follows from the first law of thermodynamics.
Further applications of the first law are made throughout the remaining chapters of the
synopsis.
It was pointed out before that, when a closed system passes through a cycle, usually

 L  0 and  Q  0 (1.39)


Many experiments show, however, that if the net work of a cycle is zero, then the net
heat transfer of that cycle is also zero. Further experiments show that whenever there is
a net work input to a closed system during a cycle, there must be a net heat transfer
from the system. Conversely, a net work output from a closed system during a cycle is
always accompanied by a net heat input. These experimental observations suggest that
there is a relationship between work and heat. Let us consider some experiments which
might be useful in a search for such a relationship.

19