Designing safe boilers depends on knowing how steam behaves under certain changes in temperature and pressure. Steam tables, such as the one below, are published giving values of the function V = f(T, P) where V is the volume (in cubic feet) of one pound of steam at a temperature of T (in degrees Fahrenheit) and pressure P (in pounds per square inch). T//P 480 500 520 540 20 22 24 26 27.85 25.31 23.19 21.39 28.46 25.86 23.69 21.86 29.06 26.41 24.20 22.33 29.66 26.95 24.70 22.79 a) Find the tangent plane to V = f(T, P) for T near 520°F and P near 24 lb/in². [Hint: Use the tables to approximate your partial derivatives and recall the equation of our tangent plane is: V = VT(T − To) + Vp(P - Po) + f(T, P) ] a b) Use the tangent plane to estimate the volume of a pound of steam at a temperature of 525°F and P near 24.3 lb/in².

Designing safe boilers depends on knowing how steam behaves under certain changes in temperature and pressure. Steam tables, such as the one below, are published giving values of the function V = f(T, P) where V is the volume (in cubic feet) of one pound of steam at a temperature of T (in degrees Fahrenheit) and pressure P (in pounds per square inch). T//P 480 500 520 540 20 22 24 26 27.85 25.31 23.19 21.39 28.46 25.86 23.69 21.86 29.06 26.41 24.20 22.33 29.66 26.95 24.70 22.79 a) Find the tangent plane to V = f(T, P) for T near 520°F and P near 24 lb/in². [Hint: Use the tables to approximate your partial derivatives and recall the equation of our tangent plane is: V = VT(T − To) + Vp(P - Po) + f(T, P) ] a b) Use the tangent plane to estimate the volume of a pound of steam at a temperature of 525°F and P near 24.3 lb/in².

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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