When a thermodynamic system undergoes a physical change in such a way that its temperature remains constant, then the change is known as isothermal changes.
(1) Essential conditions for isothermal process
(i) The walls of the container must be perfectly conducting to allow free exchange of beat between the gas and its surrounding.
(2) Equation of state : In this process. P and V change but T = constant, i.e. change in temperature ∆T = 0
Boyle’s law is obeyed, i.e. PV = constant → P1V1 = P2V2
(4) Indicator diagram : According to PV = constant, graph between P and V is a part of rectanglular hyperbola, The graphs at different temperatures parallel to each other are called isotherms.
T1 < T2 < T3
Two isotherms never intersect
(i) Slope of isothermal curve : By differentiating PV = constant, we get
P dV + V dP = 0
→ PdV = – VdP
→ Slope = tan =dPdV = – PV
(5) Specific heat : Specific heat of gas during isothermal change is infinite. As C = Q/m∆T = Q/m×0 = ∞
P dV + V dP = 0 [As ∆T = 0]