For a RC circuit, we can use Laplace transforms to show that when we apply a step input of 5V, the voltage across the capacitor rises exponentially to a final value equal to step input. Now, suppose that an initial voltage of 1V is present at the capacitor at zero time (t = 0). Will the behavior of the circuit when a step input is applied still yield an exponential rise or will the behavior be of some other type? Prove by solving the equations using Laplace transform

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.