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.
    P-V Indicator Digram in case of expansion
  • In case of compression system at state A(P1 V1) goes to a state B(P2V2) its indicator digram is as follows.

    P-V Indicator Digram in case of compression
  • 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

    Work in volume changes
    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
         W=∫PdV                         (2)
    where limits of integration goes from V1 to V2
    Graphically this relationship is shown below

    PV diagram showing the workdone
  • 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

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page

link to us