Isothermal Process (Constant Temperature 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 isothermal process. This will happens 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 isothermal process:

• there is no change in temperature (T₂ = T₁)
• there is no change in internal energy (ΔU = 0)
  

• P,V,T Relationship:

                                    PV = Constant

•   Work done:

                                    W_1-2 = P₁V₁ ln (V₂/V₁)
                                               = 2.3 P₁V₁ log (V₂/V₁)

                                               = 2.3 mRT log r

• Internal Energy:

                                    dU  = mC_v (T₂-T₁)
                                    U₂ - U₁ = 0
                                     U₂ = U₁ 

• Heat Supplied:

                                    Q_1-2 = dU + W_1-2
                                    Q_1-2 = W_1-2

Where,