First Law Of Thermodynamic

 

First law of Thermodynamic

                          Thermodynamic is the branch of the physics which deals with the transformation of heat energy into mechanical energy is called thermodynamics. First law of thermodynamic is merely the  statement of the law of conservation of energy when it is stated with reference to heat energy and mechanical energy. It can be stated in the ways: “when heat energy is transformed into mechanical energy or when energy mechanical energy is converted to heat, the total amount of energy remains constant.” or “for an isolated system the sum of all forms of energy (heat and mechanical energy) remains constant.”

                           Consider a system consisting of an ideal or perfect gas which is fitted with a frictionless piston. Let ∆Q amount of heat energy is supplied to the system and the some quantity of which converts into the work ∆W, then the remaining energy (∆Q - ∆W) is retained by the system, due to which internal energy of the system changes from U₁ to U₂. It is found experimentlly that during the repetition of this process the change in internal energy (U₂ – U₁ = ∆U) does not depend upon the path adopted by the system, but it only depends upon the initial and final states of the system.

∆Q - ∆W = U₂ – U₁

∆Q - ∆W = ∆U

∆Q = ∆U + ∆W

         i.            ∆Q is taken as positive when heat enters the system and taken negative when heat leaves the system.

        ii.            ∆W is taken positive when work is done by the system and taken negative when work is done on the system.

      iii.            ∆U is taken positive when internal energy of the system increases and taken negative when internal energy of the system decreases.

Isolated System:  An isolated system is the one which has no surroundings, that is there is no flow of heat in or out from the system and hence system is not capable to do work, therefore

∆Q = 0,           ∆W = 0.

From first law of thermodynamic we get,

∆U = 0.            OR U₁ = U₂

From above result proves the law of conservation of energy, i.e. the internal energy of an isolated system cannot be changed by any process taking within the system.

Cyclic Process:  A cyclic process is the one which starts and ends up at the same state,  i.e. system finally attains its initial state:

U₁ = U₂

∆U = 0

From first law of thermodynamic we get,

∆Q = ∆W

It means that the work obtained from a cyclic system can be at maximum equal to the energy supplied to it and no machine in any number of cycles can perform more work than the energy gained by the machine. A perpetual motion machine of the first kind was the concept of an imaginary machine which could do more work than the energy gained by it. The above result of the first law proves that it is impossible to construct such a machine.

Applications of the first law of thermodynamic

1.      Isobaric Process: An isobaric procee is the one in which pressure of the system remains constant, so that the Charle’s law is applicable.

                Consider an ideal gas system enclosed in a cylinder provided with a frictionless piston. Let the system placed on a heat reservoir and let ∆Q be the amount of heat supplied to the system, due to which kinetic energy of gas molecules increases which increases the internal from U₁ to U₂.

∆U = U₂ – U₁

Also the piston of cylinder moves upward which means change in volume of system from V₁ to V₂ but pressure of system remains constant.

∆V = V₂ - V₁

Hence some work is said to be done by the system against constant pressure.

∆W = Force × Displacement

∆W = F . ∆y

∆W = PA. ∆y    [F = PA]

∆W = P∆V      [A∆y = ∆V]

∆W = P(V₂ - V₁)

∆Q = ∆U + ∆W

∆Q = ∆U + P(V₂ - V₁)

Above result shows that in an isobaric process, all heat energy gives to the system is utilized in two ways. One in increasing the internal energy of the system and second in doing some work done against external pressure. The Graph of an isobaric process is a straight horizontal line called as an Isobar.

1.      IsoChoric Process:  An isochoric process is the one in which volume of the system remains constant, so that the pressure law is applicable.

         Consider a system of an ideal gas in a cylinder provided with a piston which is fixed. Let the system is placed on a het reservoir and ∆Q be the amount of heat supplied to the system which increases the kinetic energy of gas molecules and hence internal energy of the system changes from U₁ to U₂.(  ∆U = U₂ – U₁).  As piston can not move, therefore  there will be no change in volume of system (∆V = 0), hence there will be no workdone by the system (∆W = 0),

∆Q = ∆U + ∆W

∆Q = ∆U + 0

∆Q = ∆U

The above result shows that in an isochoric process the heat energy given to the system does nothing, but only changes the internal energy of the system. The graph of an isochoric process is a vertical straight line called Isochor.

2.      IsoThermal Process:  An isothermal process is one in which temperature of the system remains constant, so that the Boyle’s law is applicable.

          Consider a system of a gas in a cylinder, which is provided with a frictionless movable piston. Walls of the cylinder and piston ideally heat insulating and its base is ideally heat conducting. The cylinder is placed on a heat reservoir at a temperature T₁. The gas is allowed to expand by decreasing the load on the pistonand temperature of system is maintained by supplying some heat energy to the system from heat reservoir. Such an expansion is called Isothermal Expantion.

U₂ = U₁ (∆U = 0)

∆Q = ∆U + ∆W

∆Q = 0 + ∆W

∆Q = ∆W

The above result shows that in an isothermal process the heat energy given to the system is converted all into doing some work.

             If the cylinder is placed on a cold reservoir at a temperature T₂, then the gas is allowed to compressed by increasing the load on the piston. The temperature of the system is maintained by allowing the heat to leave out from the system to the surroundings. Such a contraction is called Isothermal Contraction.

-∆Q = -∆W

∆Q = ∆W

The graph of an isothermal process is a smooth curve called as isotherm.

3.      Adiabatic Process:  An adiabatic process is one in which system has no surroundings that is no heat can flow in or out from the system.

              Consider a system of a gas in cylinder provided with a movable frictionless piston. Let the system was initially at temperature T₁. Now let the system is placed on insulator and the gas expands and cools off adiabatically and its temperature falls to T₂. Thus some internal energy of the system converts into work done.

∆Q = 0

∆Q = ∆U + ∆W

0 = ∆U + ∆W

-∆U = ∆W

Above equation shows that in an adiabatic process, work is done at the cost of internal energy of the system. This process is called Adiabatic Expansion.

If the system was initially at temperature T₂ and then it is placed on insulator then the gas compresses and its temperature rises. Thus the gas at the cost of its internal energy does some work. This process is called Adiabatic Compression. The graph of an adiabatic process as a smooth curve called as adiabatic curve.