Work Done In Isothermal Process W Nrt Ln V V — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Work Done in Isothermal Process (W = nRT ln(V₂/V₁)) Applies strictly to Ideal Gases undergoing a reversible isothermal (constant temperature) process. Start with definition of work: dW = P dV Substitute P from Ideal Gas Law: P = nRT/V Integrate dW from Vi to Vf: W = ∫(nRT/V) dV Since n, R, T are constants, pull them out: W = nRT ∫(1/V) dV Solve integral: W = nRT [ln(V)] from Vi to Vf Apply limits: W = nRT (ln(Vf) - ln(Vi)) = nRT ln(Vf/Vi) Temperature T must be constant (dT = 0). Gas must behave ideally (PV=nRT applies). Process must be reversible (quasi-static). Temperature must be in Kelvin. Using degrees Celsius for Temperature instead of Kelvin. Thinking work is zero because internal energy change is zero (First Law: Q = W, dU = 0). Inverting the volume ratio (ln(Vi/Vf) calculates work done ON the gas, not BY the gas). Applying this formula to adiabatic or isochoric processes.