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
Related questions
Question
![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) ]
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa83fb5ef-60db-4fe2-ade5-42757b99636b%2F0bfc59ad-2d8b-421f-ae66-5c0ffb38c1fb%2Fb0uzuhn_processed.png&w=3840&q=75)
Transcribed Image Text: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) ]
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.
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