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2. Analyzing of the ideal gas main thermodynamic processes
In analyzing thermodynamic processes we try to determine changing variables of state
(thermodynamics co-ordinates) thermodynamic system and performance of some work
and transfer of some heat.
There are next thermodynamic processes (TP):
1. At constant volume – isochoric
2. At constant pressure – isobaric
3. At constant temperature – isothermal
4. Without exchange a heat between system and environment – adiabatic
5. Polytrophic

2.1 Thermodynamic process at constant volume
Suppose the position of the piston in fig 6 is kept fixed at one place, so that the
volume of the gas remains constant, equal to say V. If we heat or cool the inside gas its
temperature and pressure will change (fig 6). The initial state of the gas is representing
by the point 1 (with P 1, T 1 and V) and final state by the point 2 (P 2, T 2, V). For those
points we have two equations of state: VP  RT ; VP  RT . If they divide we get:
1 1 2 2
P T
2 2
 (2.1)
P 1 T 1

For this process dV  0, so no work is done by the gas l 0, and all heat is used for
changing of internal energy

du = Cv(T 2 – T 1) (2.2)

The change of the enthalpy and entropy express by the equations

dh = Cp(T 2 – T 1) (2.3)

T P
 s  C ln 2 ; s  C ln 2 (2.4)
  m   m
T 1 P 1

2.2 Thermodynamic process at constant pressure
Fig. 2.1 – isochoric TP
Suppose we heat or cool the inside gas (fig.1.3). Its temperature
and volume will change, but pressure remains constant (fig. 2.2).
For this process:

PV  RT ; PV  RT
1 1 2 2
V T
2
 2 (2.5)
V T
1 1
Work is expressed:

l  ( P V  V 1 )  T ( R 2  T 1 ) (2.6)
2
P
Quantity of heat we can determine from equation:

Fig. 2.2 – isobaric TP q  C P T ( 2  T 1 ) (2.7)
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