Work Done in Isothermal Expansion - NEET Notes, Formula & Common Mistakes
Work done in Isothermal ExpansionThermodynamicsNEET ChemistryNEET 2025First Law ThermodynamicsIsothermal Process
Work Done in Isothermal Expansion - NEET Notes, Formula & Common Mistakes
Thermodynamics·2 min read·NEET 2026
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 moles
R = gas constant (8.314 J K⁻¹ mol⁻¹ or 0.0821 L atm K⁻¹ mol⁻¹)
T = constant temperature in Kelvin
V₁, V₂ = initial and final volumes
P₁, 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.
Frequently Asked Questions
What is an isothermal process in thermodynamics?▾
An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout. This means the change in temperature, ΔT, is zero.
Why is ΔU = 0 for an ideal gas in an isothermal process?▾
For an ideal gas, internal energy (U) is solely a function of temperature. Since the temperature (T) remains constant in an isothermal process (ΔT=0), the internal energy of an ideal gas also remains unchanged, meaning ΔU = 0.
What is the sign convention for work done in expansion?▾
In chemistry, the convention for work done is that work done *by* the system on the surroundings (e.g., expansion) is negative (W < 0). Conversely, work done *on* the system by the surroundings (e.g., compression) is positive (W > 0).
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