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Isothermal

An isothermal process occurs at constant temperature.  Since the internal energy of a gas is only a function of its temperature, ΔU = 0 for an isothermal process.  For the isothermal expansion of an ideal gas we have W = nRT ln(V2/V1).  W is positive if V2 > V1.  Since ΔU = 0, the heat transferred to the gas is ΔQ = W.

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Thermodynamics

By Zach grocke