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Isothermal Process

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.
In this process, P and V change but T = constant, i.e., change in temperature ΔT = 0

Essential conditions for isothermal process

  • The walls of the container must be perfectly conducting to allow free exchange of heat between the gas and its surrounding (Fig. 6).
Fig. 6
  • The process of compression or expansion should be so slow so as to provide time for the exchange of heat.
    Since these two conditions are not fully realized in practice, therefore, no process is perfectly isothermal.
Equation of state From ideal gas equation, PV = μRT. If temperature remains constant, then PV= constant, i.e., in all isothermal processes Boyle’s law is obeyed.
Hence, equation of state is PV = constant.

Indicator diagram

  • Curves obtained on PV graph are called isotherms and they are hyperbolic in nature.
  • Slope of isothermal curve: By differentiating PV = constant, we get PdV + V dP = 0
Fig. 7
  • Area between the isotherm and volume axis represents the work done in isothermal process.
    If volume increases ΔW = +(Area under curve) and if volume decreases ΔW = –(Area under curve).
Isothermal elasticity For isothermal process PV = constant.
Differentiating both sides
∴ Eθ = P, i.e., isothermal elasticity is equal to pressure.
At NTP, isothermal elasticity of gas = Atmospheric pressure = 1.01 × 105 N/m2
Work done in isothermal process
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