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.
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
dW = PAdx
= PdV (1)
since V = Adx and dV is change in volume of the system.
- In a finite volume change from V1 to V2
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.
:Work done in a process is given by area under the process on the PV diagram
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