First law of thermodynamics:-

  Statements

1)   The energy is neither be created nor be destroyed , it just converted from one form to other form.

2)  Total energy of the universe is always constant.

3) Whenever amount of energy of one form (kind)disappears , an exactly equivalent amount of energy of other kind is appear

4)   Total internal energy of an isolated system is constant.

Mathematical Equation of first law of thermodynamics

Suppose q quantity of heat is supplied to the system and W is Work done on the system by surrounding and internal energy change from U₁ toU₂Hence increases in internal energy of a system.

Final internal energy = Initial internal energy + heat absorbed + Work done by surrounding

U₂   = U₁ + q + W

U₂ – U₁ = q + W

∆U = q + W

Where ∆U = Increases in internal energy

             U₁= initial internal energy

             U₂ = final energy

             q = heat absorbed by the system

             w = Work done on the system.

For small change equation will be

                    du = dq + dw

                         OR                                                                                                                  dq = du – dw

          du = small increases in internal energy

          dq = small amount of heat supplied to the system

          dw = small amt. of work done

                  

Corollary: - Heat and other form of energies can be quantitatively converted into work

Modification of 1^st law of thermodynamics:-

                   A/C to Einstein’s equation E = mc², mass is also converted into energy Therefore modification for 1^st law of thermodynamics is

 “The total mass and energy together of an isolated system is always remain constant.”

First law of thermodynamics for various systems:-

i)            For isothermal process:-

For such process, temp is const and internal energy is also constant

          ∆T =0

          ∆U = 0

Mathematical expression for 1^st law of thermodynamics’

          ∆U = q +w

          0 = q + w

          W = -q  

Or      q = -W

Hence in isothermal process heat absorbed is entirely used for doing work on the surrounding or that work on the system by the surrounding. result is release of heat by the system.

ii)          Adiabatic process :-

        In adiabatic process No exchange of heat between the system and surrounding that is q=0

                            ∆U = W + q

                            ∆U = W + 0

∆U = W

          Hence in adiabatic process increases in internal energy of the system due to the work done on the system by surrounding or work done by the system on the surrounding is due to the expense of the system internal energy which decreases in the process.

iii)         Isochoric process :-

          In isochoric process ∆V = 0

                            ∆U = q + W

                            ∆U = q – P_ex (∆V)

∆U = q_V 

          Hence in isochoric process change in internal energy of the system is due to the heat transfer.

         V is a state function q_V is also state function

iv)          Isobaric process:-

          In isobaric process ∆P = 0, ∆V≠ 0

Mathematical equation for 1^st of thermodynamic

                            ∆U = q + W

                            ∆U = q – P_ex ( ∆V)

∆U = q_P – P_ex  x ∆V

∆U + P_ex . ∆V = q_P

                             q_P = ∆U + P_ex  ∆V

Sign convention of W and q

 +q = Heat absorbed by the system from the surrounding.

 -q = Heat Released from the system and flow to the surrounding.

 +W = Work is done on the system by the surrounding e.g. Work of 

            compression

  -W  = Work is done by the system on the surrounding. E.g. Work of expansion

 ∆U = +ve then increases in internal energy

 ∆U = -ve then decreases in internal energy