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2) Operating a steady-state, a well insulated mixing chamber receives two input liquid streams of the...

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Physics

2) Operating a steady-state, a well insulated mixing chamberreceives two input liquid streams of the same substance but withtemperatures T1 and T2 and mass flow rates m ̇ 1 and m ̇ 2respectively. The streams are mixed in the chamber, exiting as asingle stream with T3 and m ̇ 3. Assuming the substance isincompressible with constant specific heat C, that potentialenergy, kinetic energy, and pressure changes are negligible, obtainan expression for

a) T3 in terms of T1, T2 and the ratio of the mass flow rates ṁ 1/m ̇ 3.

b) the rate of entropy production per unit mass exiting thechamber in terms of C, T1/T2 and m ̇ 1/m ̇ 3.

c) For fixed values of C and T1/T2, determine the value for m ̇1/m ̇ 3 for which the rate of entropy production per unit mass out,σ ̇/m ̇3, is a maximum. (Hint start with an expression for σ ̇/m ̇3as a function of m ̇ 1/m ̇ 3.)

NOTE: m * = M (Dot)

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