Constant Temperature Process (Isothermal Process)

A process, in which the temperature of the working substance remains constant during its expansion or compression, is called a constant temperature process or iso-thermal process. This will happen when the working substance remains in a perfect thermal contact with the surroundings, so that the heat 'sucked in' or 'squeezed out' is compressed exactly for the mechanical work done by or on the gas respectively. It is thus obvious that in an iso-thermal process:

1. there is no change in temperature, and
2. there is no change in internal energy

i) P,V,T Relationship:
                                    PV = Constant
ii) Work done:

                                    W_1-2 = P₁V₁ ln (V₂/V₁)

                                               = 2.3 P₁V₁ log (V₂/V₁)

                                               = 2.3 mRT log r

iii) Internal Energy:
                                    dU  = mC_v (T₂-T₁)
                                    U₂ - U₁ = 0
                                     U₂ = U₁ 

iv) Heat Supplied:
                                    Q_1-2 = dU + W_1-2
                                    Q_1-2 = W_1-2

Where,