To identify how much heat is required to bring a kettle of water to its boiling point, you are required to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table Q1(a). Q1 _(a) Table Q1(a): Specific heat of water as a function of temperature Temperature, T Specific heat, C, (C) J kg-°C) 42 4179 52 4186 82 4199 100 4217 110 4300 (i) Determine the value of the specific heat at T = 61°C using a second order Lagrange polynomial. (ii) Determine the value of the specific heat at T = 61°C using a third order Lagrange polynomial. Find the absolute relative approximate error e. obtained between the results from the second with third order polynomial. (iii)
To identify how much heat is required to bring a kettle of water to its boiling point, you are required to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table Q1(a). Q1 _(a) Table Q1(a): Specific heat of water as a function of temperature Temperature, T Specific heat, C, (C) J kg-°C) 42 4179 52 4186 82 4199 100 4217 110 4300 (i) Determine the value of the specific heat at T = 61°C using a second order Lagrange polynomial. (ii) Determine the value of the specific heat at T = 61°C using a third order Lagrange polynomial. Find the absolute relative approximate error e. obtained between the results from the second with third order polynomial. (iii)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q1 (a)
To identify how much heat is required to bring a kettle of water to its boiling point,
you are required to calculate the specific heat of water at 61°C. The specific heat of
water is given as a function of time in Table Q1(a).
Table Q1(a): Specific heat of water as a function of temperature
Temperature, T Specific heat, C,
(C)
J
kg-°C )
42
4179
52
4186
82
4199
100
4217
110
4300
(i)
Determine the value of the specific heat at T = 61°C using a second order
Lagrange polynomial.
(ii)
Determine the value of the specific heat at T = 61°C using a third order
Lagrange polynomial.
Find the absolute relative approximate error e, obtained between the results
from the second with third order polynomial.
(iii)
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