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An isothermal process occurs at constant temperature ($\Delta T = 0$). For an ideal gas, this means $\Delta U = 0$, so the First Law simplifies to $Q = W$ — all heat absorbed converts entirely to work (or vice versa). The equation of state gives Boyle's law: $P_1V_1 = P_2V_2$.

Work done in an isothermal process: $W = nRT\ln(V_2/V_1) = nRT\ln(P_1/P_2)$. For expansion ($V_2 > V_1$), $W > 0$ and the gas absorbs heat from the surroundings to maintain constant temperature. For compression, work is done on the gas and heat is released.

On a P-V diagram, an isothermal curve is a rectangular hyperbola ($PV = \text{constant}$). The slope at any point is $dP/dV = -P/V$. An isothermal process requires two conditions: the system must be in thermal contact with a heat reservoir, and the process must be quasi-static (slow enough for temperature equilibrium at each step).

The specific heat during an isothermal process is effectively infinite: $C_T = Q/(n\Delta T) = Q/0 \to \infty$. This makes physical sense — you can add heat without changing temperature because it all converts to work.