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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.
    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.
    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
              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


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