3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x, t) if the bar is made of cast iron. Material a² (cm³/s) Silver 1.71 Copper Aluminum 1.14 0.86 0.12 0.011 Cast iron Granite Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materials

3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x, t) if the bar is made of cast iron. Material a² (cm³/s) Silver 1.71 Copper Aluminum 1.14 0.86 0.12 0.011 Cast iron Granite Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materials

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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Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.

Question

3.
A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends
of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an
expression for the temperature u(x, t) if the bar is made of cast iron.
Material
a (cm²/s)
Silver
1.71
Copper
1.14
Aluminum
0.86
Cast iron
0.12
Granite
0.011
Brick
0.0038
Water
0.00144
Table 1: Thermal Diffusivity Constants for Common Materials

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