At a given instant of time, the temperature distribution within an infinite homogeneous body is given by the function T(x, y, z)=x^2-2 y^2 z^2-x y 2 y z Assuming constant properties and no internal heat generation, determine the regions where the temperature changes with time. | Numerade

SOLVED:For a homogeneous (single-phase) simple pure substance, the pressure and temperature are independent properties, and any property can be expressed as a function of these two properties. Taking U=U(P, T), show that the change in specific volume can be expressed in terms of the volume expansivity βand isothermal compressibility αas (d U)/(U)=βd T=αd P Also, assuming constant average values for βand α, obtain a relation for the ratio of the specific volumes U2 / U1 as a homogeneous system un

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