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, Cp (°C) J kg-°C j 42 4187 52 4194 82 4207 100 4225 110 4308 Determine the value of the specific heat at T = 61°C using a second order Lagrange polynomial. (i) Determine the value of the specific heat at T = 61°C using a third order Lagrange polynomial. (ii) Find the absolute relative approximate error . 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). Table Q1(a): Specific heat of water as a function of temperature Temperature, T Specific heat, Cp (°C) J kg-°C j 42 4187 52 4194 82 4207 100 4225 110 4308 Determine the value of the specific heat at T = 61°C using a second order Lagrange polynomial. (i) Determine the value of the specific heat at T = 61°C using a third order Lagrange polynomial. (ii) Find the absolute relative approximate error . 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, Cp
(°C)
J
kg-°C )
42
4187
52
4194
82
4207
100
4225
110
4308
Determine the value of the specific heat at T = 61°C using a second order
Lagrange polynomial.
(i)
(ii)
Determine the value of the specific heat at T = 61°C using a third order
Lagrange polynomial.
Find the absolute relative approximate error . obtained between the results
from the second with third order polynomial.
(iii)
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