MAE 240 - Summer 2016 Homework 2 - Due 5/27/2016 Polytropic processes of ideal gases, additional practice using the first law, and heat transfer 1. Oxygen at 101325 kPa and 25 is contained in a piston-cylinder assembly with an initial volume of 1200 3 . The oxygen is compressed slowly and adiabatically to a final volume of 400 3. Assume that oxygen under these conditions has a constant specific heat. Find the following: A. The final temperature; B. The final pressure; C. The work done during the compression process. 2. Air is slowly expanded at constant pressure from an initial temperature of 330 K to a final temperature of 800 K in a piston-cylinder assembly. The initial volume of air is 350 cm3 and the pressure is 112 kPa. Calculate the work done and the heat transferred assuming a constant specific heat. 3. Assume that 1 kg of liquid water at a temperature of 100 is to be converted into steam at atmospheric pressure of = 101325 . During this process, the volume of the water changes from an initial value of approximately 1.00 103 3 as a liquid to approximately 1.671 3 as steam. A. How much work is done by the system in this process? B. Given the latent heat of evaporation for water in this process is approximately = 2256 , find the heat transferred to the water during this process. C. What is the change in the internal energy of the water during this process? 4. The wall of a furnace is a large surface of fire clay brick, which is 6.5 cm thick. The outer surface of the brick is required to be less than 35 C for the safety of the operations personnel. The inner surface receives a heat flux of 2.3 W/cm2. A. What is the peak allowable internal temperature of the furnace? You may assume that the fire clay brick has a constant thermal conductivity of = 1.395 . B. If the internal temperature is required to reach 2000 K, what thickness of brick would be required to maintain the outer surface at the safety limit of 35 C? 5. The sun can be approximated as a spherical black body with a surface temperature of 5762 K. The irradiation from the sun as measured by a satellite in earth orbit is 1353 W/m2. The distance from the earth to the sun is approximately 1.5 x 1011 m. Assuming that the sun radiates evenly in all directions, estimate the diameter of the sun. 6. A metal plate 16 cm by 8 cm is placed outside on a clear night. The plate, which has an emissivity of 0.71, exchanges heat by radiation with the night sky, which is at 45. Air at 12.5 flows over the top of the plate, cooling it with a heat transfer coefficient of 40 2 . The plate is insulated on its underside and heated by an electric resistance heater. How much electric power must be supplied to maintain the plate at 53