Liquid methane is to be converted into gas for insertion into the natural gas pipeline by a steady-state gasification plant. The methane will enter the plant as a saturated liquid at 1 atmosphere (state 1: very cold) and will leave at the environment temperature T₀ and pipeline pressure P_0?(state 2). The device will use a heat exchanger to take energy from the environment. Starting from basic principles, derive an expression for the maximum amount of useful shaft power W? that could be generated by such a plant. Express your result in terms of thermodynamic properties at states 1 and 2. Assume steady-state, negligible kinetic and potential energies, and one-dimensional flow at states 1 and 2.

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M W plant To Qo -M