Let Q and W denote the amount of heat given to an ideal gas and the work done by it in an isothermal process.

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Q = W In an isothermal process, temperature of the system stays constant, i.e. there's no change in internal energy. Thus, U = 0, where U denotes the change in internal energy of the system. According to the first law of thermodynamics, heat supplied to the system is equal to the sum of change in internal energy and work done by the system, such that Q = U + W. As U = 0, Q = W.

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