1. The specific heat capacity C,J/mol/°C] is often correlated to temperature T[°C] in form of a polynomial as C, = a + bT + cT² + dT³ Where a, b, c, and d are all empirical constants. For water under 500 kJ heat is provided to 10 mole air (79% nitrogen, 21% oxygen) at 20°C. Use the root-finding methods (bisection, false position, fixed point and Newton's method) to find out the final temperature of air. Which root-finding method shows the fastest convergence rate in this problem? Constants for oxygen: a = 29.1, b = 1.158 * 10-2, c = -0.6076 * 10-5, d = 1.311 * 10-9 Constants for nitrogen: a = 29, b = 0.2199 * 10-2, c = 0.5723 * 10-5, d = -2.871 * 10-9

1. The specific heat capacity C,J/mol/°C] is often correlated to temperature T[°C] in form of a polynomial as C, = a + bT + cT² + dT³ Where a, b, c, and d are all empirical constants. For water under 500 kJ heat is provided to 10 mole air (79% nitrogen, 21% oxygen) at 20°C. Use the root-finding methods (bisection, false position, fixed point and Newton's method) to find out the final temperature of air. Which root-finding method shows the fastest convergence rate in this problem? Constants for oxygen: a = 29.1, b = 1.158 * 10-2, c = -0.6076 * 10-5, d = 1.311 * 10-9 Constants for nitrogen: a = 29, b = 0.2199 * 10-2, c = 0.5723 * 10-5, d = -2.871 * 10-9

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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Question

1. The specific heat capacity C,J/mol/°C] is often correlated to temperature T[°C] in form
of a polynomial as
C, = a + bT + cT² + dT³
Where a, b, c, and d are all empirical constants. For water under
500 kJ heat is provided to 10 mole air (79% nitrogen, 21% oxygen) at 20°C. Use the root-finding
methods (bisection, false position, fixed point and Newton's method) to find out the final
temperature of air. Which root-finding method shows the fastest convergence rate in this
problem?
Constants for oxygen:
a = 29.1, b = 1.158 * 10-2, c = -0.6076 * 10-5, d = 1.311 * 10-9
Constants for nitrogen:
a = 29, b = 0.2199 * 10-2, c = 0.5723 * 10-5, d = -2.871 * 10-9

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