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Heat (ΔQ)

Heat is the energy that is transferred between a system and its environment because of the temperature difference between them. Heat always flow from a body at higher temperature to a body at lower temperature till their temperatures become equal.
For gases, when heat is absorbed and temperature changes:

Work (ΔW)

Work can be defined as the energy that is transferred from one body to the other owing to a force that acts between them.
If P be the pressure of the gas in the cylinder, then force exerted by the gas on the piston of the cylinder F PA (Fig. 1).
Fig. 1
In a small displacement of piston through dx, work done by the gas
dW = F ⋅ dx = PA dx = P dV
∴ Total amount of work done,


Important Points
  • Like heat, work is also a path-dependent, scalar physical quantity with dimension [ML2T –2].
  • From ΔW = P ΔV = P(Vf – Vi),
    ΔW = positive if Vf > Vi, i.e., system expands against some external force.
    ΔW = negative if Vf < Vi i.e., system contracts because of some external force exerted by the surrounding.
  • In P–V diagram or indicator diagram, the area under P–V curve represents work done (Fig. 2).
    Fig. 2
    W = area under P–V diagram
    It is positive if volume increases (for expansion).
    It is negative if volume decreases (for compression).
  • In a cyclic process, work done is equal to the area under the cycle.
    Fig. 3
    It is positive if the cycle is clockwise.
    It is negative if the cycle is anticlockwise.
    From this equation, it seems as if work done can be calculated only when P–Vequation is known and limits Vi and Vf are known to us.
    If massless piston is attached to a spring of force constant K, a mass m is placed over the piston, the external pressure is P0, and due to expansion of gas the piston moves up through a distance x, then
    Fig. 4
    Total work done by the gas W = W1 +W2 + W3hd
      W1 = Work done against external pressure (P0)
      W2 = Work done against spring force (Kx)
      W3 = Work done against gravitational force (mg)
      ∴ 56151.png
  • If the gas expands in such a way that other side of the piston is vacuum (Fig. 5), then the work done by the gas will be zero.
    As W = P ΔV = 0 [here P = 0]
    Fig. 5

Internal energy (U)

Internal energy of a system is the energy possessed by the system due to molecular motion and molecular configuration.
The energy due to molecular motion is called internal kinetic energy UK and that due to molecular configuration is called internal potential energy UP.
i.e., Total internal energy, U = U + UP
  • For an ideal gas, as there is no molecular attraction, UP = 0, i.e., internal energy of an ideal gas is totally kinetic and is given by
    and change in internal energy 55792.png 
  • In case of gases whatever be the process,
  • Change in internal energy does not depend on the path of the process. So it is called a point function, i.e., it depends only on the initial and final states of the system, i.e., ΔU = Uf – Ui
  • Change in internal energy in a cyclic process is always zero as for cyclic process Uf = Ui
    So ΔU = Uf – Ui = 0

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