please complete #6

parts a through c

part b find temperature at t=5 and

skip part b (ii-v)

part c - base your answer on calculations in part a

6. A spherical ball is taken out of a furnace at 2500 K. It loses heat due to radiation and convection. Given the following, Radius of ball, r = 1.0 cm Density of the ball, p = 3000 kg/m' Specific heat, C = 1000 J/(kg.K) Emittance, E=0.5 Stefan-Boltzmann Constant, 0 = 5.67x10-*J/(s.mK) Convective cooling coefficient, h = 500 J/(s.m? .K) Initial temperature of the ball, 0(0) = 2500 K, Ambient temperature, 0, = 300 K, the ordinary differential equation that governs the temperature of the ball is given by de = -2.8349x10-2 (0' - 81x10%) - 0.05 (0-300). di Hint: The above formula was calculated by using the knowledge that Rate of heat lost due to radiation = A 0(04-0) Rate of heat lost due to convection = hA(0-0) Heat stored = mco where A = surface area of the ball, m=mass of the ball. a) What are following at i = 0 s? i. temperature, ii. rate of change of temperature, iii. rate of heat loss due to radiation, iv. rate of heat loss due to convection, V. rate of heat stored. b) Find the following at 1 =10 s using Euler's method and a step size of h=2.5. i. temperature, ii. rate of change of temperature, iii. rate of heat loss due to radiation, iv. rate of heat loss due to convection, v. rate of heat stored. c) Can either convection or radiation be neglected if we are interested in finding the temperature profile between 0 and 10 s? Base your answer on quantitative reasoning