18. Let a metallic rod 20 cm long be heated to a uniform temperature of 100°C. Suppose that at t = 0 the ends of the rod are plunged into an ice bath at 0°C, and thereafter main- tained at this temperature, but that no heat is allowed to es- cape through the lateral surface. Find an expression for the temperature at any point in the rod at any later time. Deter- mine the temperature at the center of the rod at time t = 30 s if the rod is made of (a) silver, (b) aluminum, or (c) cast iron.
18. Let a metallic rod 20 cm long be heated to a uniform temperature of 100°C. Suppose that at t = 0 the ends of the rod are plunged into an ice bath at 0°C, and thereafter main- tained at this temperature, but that no heat is allowed to es- cape through the lateral surface. Find an expression for the temperature at any point in the rod at any later time. Deter- mine the temperature at the center of the rod at time t = 30 s if the rod is made of (a) silver, (b) aluminum, or (c) cast iron.
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Transcribed Image Text:18. Let a metallic rod 20 cm long be heated to a uniform
temperature of 100° C. Suppose that at t= 0 the ends of the
rod are plunged into an ice bath at 0°C, and thereafter main-
tained at this temperature, but that no heat is allowed to es-
cape through the lateral surface. Find an expression for the
temperature at any point in the rod at any later time. Deter-
mine the temperature at the center of the rod at time t = 30 s
if the rod is made of (a) silver, (b) aluminum, or (c) cast
iron.
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Step 1: Determine the given data:
VIEWStep 2: Determine the expression of temperature at any value of x and t:
VIEWStep 3: Determine the temperature at the center of the rod at t=30 sec for silver:
VIEWStep 4: Determine the temperature at the center of the rod at t=30 sec for Aluminum:
VIEWStep 5: Determine the temperature at the center of the rod at t=30 sec for cast iron:
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