(a) Show that if A is a constant and when 0...

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(a) Show that if A is a constant and when 0 <x < S(x) = when the temperature formula in Problem 4(b) becomes 4A sin? (nT/4) Σ u(x,1) = exp sin (b) Two slabs of iron (k 0.15 cgs unit), each 20 cm thick, are such that one is at 100°C and the other at 0°C throughout. They are placed face to face in perfect contact, and their outer faces are kept at 0°C. Use the result in part (a) here to show that the temperature at the common face 10 min after contact has been made is approximately 36°C. Then show that if the slabs are made of concrete (k = 0.005 cgs unit), it takes approximately 5 h for the common face to reach that temperature of 36°C. [Note that u(x, t) depends on the product kt.] (a) Show that if A is a constant and when 0 <x < S(x) = when the temperature formula in Problem 4(b) becomes 4A sin? (nT/4) Σ u(x,1) = exp sin (b) Two slabs of iron (k 0.15 cgs unit), each 20 cm thick, are such that one is at 100°C and the other at 0°C throughout. They are placed face to face in perfect contact, and their outer faces are kept at 0°C. Use the result in part (a) here to show that the temperature at the common face 10 min after contact has been made is approximately 36°C. Then show that if the slabs are made of concrete (k = 0.005 cgs unit), it takes approximately 5 h for the common face to reach that temperature of 36°C. [Note that u(x, t) depends on the product kt.]

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