# Thermodynamics

## 3. P-V Indicator Digram

• Only two thermodynamic variables are sufficient to describe a system because third vaiable can be calculated from equation of state of the system.
• P-V Indicator Digram is just a graph between pressure and volume of a system undergoing an operation.
• When a system undergoes an expansion from state A (P1 V1) to a state B (P2V2) its indicator digram is shown as follows.

• In case of compression system at state A(P1 V1) goes to a state B(P2V2) its indicator digram is as follows.

• Intermediate states of system are represented by points on the curve.
• The pressure volume curve for a fixed temperature is called isotherm.

## 4. Work in volume changes

• Consider a cylinder filled with gas and equiped with a movable piston as shown in fig below

fig - Force exerted by a system during small expansion.
Suppose,
A - Cross Sectional area of cylinder
P - Pressure exerted by piston at the piston face.
PA - Force exerted by the system.
• If piston moves out by a distance dx then work done by this force is dW given by
= PdV                    (1)
since V = Adx and dV is change in volume of the system.
• In a finite volume change from V1 to V2
W=∫PdV                         (2)
where limits of integration goes from V1 to V2
Graphically this relationship is shown below

• Thus eqn (2) can be interpreted graphically as area under the curve between limits V1and V2.
• If pressure remains constant while the volume changes, then work is
W = P(V2-V1)          (3)
• Work done not only depends on initial and final states but also on the intermediate states i.e., on the path.
Learning:Work done in a process is given by area under the process on the PV diagram