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Isothermal expansion

From the first law of thermodynamics,
ΔE = q + w
For isothermal process, ΔE = 0. Hence,
q = –w
In the case of isothermal expansion, work is done by the system at the cost of heat absorbed. The magnitude of q or w depends on the manner in which the process of expansion is carried out, i.e., reversibly or irreversibly.
ΔH can be calculated as follows:
ΔH = ΔE + ΔngRT
For isothermal process, ΔE = 0 and ΔT = 0; thus, ΔH = 0.
Work done in reversible isothermal expansion
Work done in reversible isothermal expansion is given by
Description: 45356.png
At constant temperature, Description: 45363.png
∴ wrev = –2.303 nRT log10Description: 45372.png
Work done in irreversible isothermal expansion
Irreversible isothermal expansions observed are (i) free expansion and (ii) intermediate expansion.
Since the external pressure is zero in free expansion, the work done is zero, e.g., expansion of a gas in vacuum.
The external pressure is less than gas pressure in the case of intermediate expansion. Thus, the work done when volume changes from V1 to V2 is
Description: 45380.png
Since, Pext is less than the pressure of the gas, the work done during intermediate expansion is numerically less than that during reversible isothermal expansion in which Pext is almost equal to P.

Adiabatic Expansion

From the first law of thermodynamics, ΔE = q + w.
In an adiabatic expansion, q = 0; therefore, ΔE = w.
The molar heat capacity at constant volume of an ideal gas is given by
Description: 45391.png
or dE = CV × dT
and for finite changes, ΔE = CV × ΔT = w.
The value of ΔT depends on the nature of process (i.e., reversible or irreversible).
  • Reversible adiabatic expansion
    TVΔγ – 1 = constant or PV γ = constant
  • Irreversible adiabatic expansion
    Description: 45399.png

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