A solid metal sphere with a diameter of 2 cm and a mass of 8 g is used for the following heat transfer experiments. You can assume the temperature throughout the inside of the metal sphere is uniform. a. Measurement of heat capacity of the metal. The sphere initially has a temperature of 100C and it is immersed in a well-insulated container with 0.5 L of water at 0C. After the water and metal come to equilibrium the temperature is 4.7C. Neglect any heat losses to the surroundings. What is the heat capacity of the metal? b. Measurement of convection heat transfer coefficient in a furnace. The sphere initially has a temperature of 25C and it is inserted into an oven with air temperature of 450C. After 31 seconds the temperature of the sphere is 30C. You can neglect radiation heat transfer and assume the temperature inside the sphere is uniform. What is i. the average rate of heat transfer to the sphere? ii. the average heat flux to the surface of the sphere? iii. the convection heat transfer coefficient?