You have been asked to size a water heating system for camping. the system is a simple black polyethylene bag filled with 1 gallon of water laid flat in the midday sun. the solar absorptivity of polyethylene black plastic is 0.94 and the emissivity to the sky is 0.92. the water is initially at 50°f and needs to be heated to 110°f in 4 hours. at 80°f the density of water and specific heat are 62.215 lbm/fts and 1.00 btu/lbm-°f, respectively. the radiative and convective losses will be higher at higher temperatures, as a result you will need to design the water heating bag based on the highest temperature. the bag is well insulated from the ground and there will no losses due to conduction to the ground it will be placed on folded sleeping bag). at the design conditions the convective heat transfer coefficient is 0.215 btu/ft2-h-°f, the air temperature is 60°f, the temperature of the sky is -15°f, the solar irradiation is 150 btu/ft2-h. a. how much energy is required to heat the water (btu)? b. what is the solar heat flux absorbed by the bag at design conditions (btu/h-ftz)? c. what are the convective heat flux losses of the bag at design conditions (btu/h-ft)? d. what are the radiative heat flux losses of the bag at design conditions (btu/h-ft)? e. how much usable heat flux is provided to the bag at design conditions (btu/ft2-h)? f. what should the exposed surface area of the bag be ( g. how long would it take to heat the bag if the convective heat transfer coefficient were 3 times larger (h)?