A piece of metal is heated up to 1200 C and then cooled in a pool of water to 512 C before forging. Invoke Newtons law of cooling using Euler method, assuming k = 0.01 s-1 and t = 10 s, 1 s.

Part I) How long should the 1200 C metal be immersed in the pool of water if the water temperature remains at 25 C?

Part II) How long should the 1200 C metal be immersed in the pool of water if the water temperature increases linearly from 25 C to boiling in 1123 seconds? Here, 1 , 2 , 3 are the largest, second largest, and third largest digits, respectively, of your student ID. , ID = 110 733 456 gives 1 = 7, 2 = 6, and 3 = 5 and, therefore, k = 0.07 s-1, the metal cools to 576 C, and for Part II, it takes 1765 s to boil the water.

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