4. An iron bar 2cm3cm10cm at a temperature of 100C is dropped into a barrel of water at 25C. The barrel is large enough so that the increase in water temperature can be assumed as negligible. The rate at which heat is transferred from the bar to the water is given by, Q(minJ)=UA(TbTw) where U(0.05J/min.cm2C) is the heat tranfer coefficient, A(cm2) is the exposed surface area of bar, Tb is the surface temperature of bar and Tw is the temperature of water. The heat capacity of bar is 0.46J/gC and the density of bar is 7.7g/cm3. Tb(t) is to be considered uniform throughout the bar. a. Derive an expression for Tb(t) and calculate the time required for the bar to cool to 40C. b. Determine the final steady state temperature of bar