What NEET Asks
- Direct application of work done formulas for reversible and irreversible isothermal processes.
- Conceptual questions on the implications of ΔT=0 for internal energy (ΔU) of an ideal gas.
- Sign conventions for work (W) and heat (Q) are frequently tested.
Key Points
- Isothermal Process: Temperature (T) remains constant throughout the process (ΔT = 0).
- For an ideal gas undergoing an isothermal process, the change in internal energy (ΔU) is zero because internal energy depends solely on temperature.
- According to the First Law of Thermodynamics, ΔU = Q + W. Since ΔU = 0 for an isothermal process of an ideal gas, Q = -W.
- Reversible Isothermal Expansion: Work done (W) is maximum. System is always in equilibrium with surroundings.
- Irreversible Isothermal Expansion: Work done is less than reversible. Usually occurs against a constant external pressure.
Must-Know Formula / Reaction
- Work done in Reversible Isothermal Expansion:
W_rev = -2.303 nRT log(V₂/V₁) OR W_rev = -2.303 nRT log(P₁/P₂)
Where:
n= number of molesR= gas constant (8.314 J K⁻¹ mol⁻¹ or 0.0821 L atm K⁻¹ mol⁻¹)T= constant temperature in KelvinV₁,V₂= initial and final volumesP₁,P₂= initial and final pressures - Work done in Irreversible (Constant P_ext) Isothermal Expansion:
W_irr = -P_ext (V₂ - V₁)
Where:
P_ext= constant external pressure
Common Mistakes
- Students often forget that for an ideal gas, ΔU = 0 in an isothermal process, leading to incorrect calculations using ΔU = Q + W.
- Don't confuse the formulas for reversible and irreversible processes. Using P_ext for reversible work is a common error.
- Incorrectly applying the sign convention for work: work done by the system (expansion) is negative (W < 0), work done on the system (compression) is positive (W > 0).
Rapid Revision
In isothermal expansion, T is constant. For ideal gases, ΔU=0, so Q=-W. W_rev = -2.303 nRT log(V₂/V₁) or -2.303 nRT log(P₁/P₂). W_irr = -P_ext (V₂ - V₁). Always check units and sign conventions for accurate answers.