Consider the water pipe treated in Example 7.7.4. Suppose now that the water is not flowing. The water is initially at 120oF. The copper pipe is 6 ft long, with inner and outer radii of 1 /4 in. and 3/8 in. The temperature of the surrounding air is constant at 70°F. Neglect heat loss from the ends of the pipe, and use the following values. For copper, k = 50 lb/sec-oF. The convection coefficient at the inner surface between the water and the copper is now different because the water is standing. Use hi, = 6 lb/sec-ft-°F. The convection coefficient at the outer surface between the air and the copper is ho =1.1 lb/sec-ft-°F. Develop and solve a dynamic model of the water temperature T(t) as a function of time.