Quiz1s - Fall 2007 ME 416 Computer Assisted Design of...

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Fall 2007 1 ME 416 Computer Assisted Design of Thermal Systems Quiz #1 Solution A valve is often considered an isenthalpic device. Determine how a temperature change gives rise to a volume change for a valve. That is, reduce the partial derivative, h T v Solution: Following our step by step process: Step 1: Since our derivative contains the enthalpy h, we need to bring it to the numerator using Jacobian manipulations and eliminate it by use of the appropriate defining differential equation. ( 29 ( 29 h T, h v, = T v h write as Jacobian ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 P T, h T, P T, h v, h T, h v, ÷ = introduce P&T We now transform the Jacobians back to derivatives. Starting with the 1 st Jacobin, we must write out the fill determinant ( 29 ( 29 P T T P T P T P T h P v P h T v P h T h P v T v P T, h v, - =
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