4) [30] BEYOND THE TEXTBOOK A house uses propane for heating. The propane tank, a cylinder (D=0.4 m, H=1.2 m), has a pressure relief valve that releases propane into the air outside the tank if the pressure inside the tank reaches 2.8 MPa. Initially, the tank contains 50 kg of propane at 20 C. You may neglect the thermal energy of the metal tank itself. a) A fire occurs, and the tank is heated by the hot combustion products. Estimate the amount of heat transfer into the tank that can occur before the pressure relief valve starts venting. b) Sketch the process from the initial state (1) to the start of venting (2) on a p-v diagram that shows the vapor dome. c) If heat transfer occurs via convection with convective heat transfer coefficient 25 W/(m2 K) and T_surroundings =750 K, estimate how long it takes before the tank starts to vent. Neglect all heat transfer to or from the bottom of the tank. d) The pressure relief valve letting propane into a burning house sounds like a bad idea. Would the propane tank be better off without a pressure relief valve in this situation? Explain your reasoning (2-5 sentences). e) Describe one idea you have for improving the accuracy of your estimate of the time before venting. What additional information would you need to have, in order to make an improved estimate (2-5 sentences).