Problem 1) [40 pts] In order to carry out a laboratory experiment, an 8-liter water bath (initially at 25C ) must be cooled to 10C. Chilled water (the utility fluid) is available at 5C and is passed through the cooling coil ( Dtube=1cm,L=1m ) at a very high flow rate (m2). The heat transfer coefficient (U) between the utility fluid and the water bath has been measured to be 500 W/(m2K) (a) [8 pts] Assuming that the water bath is well-insulated, write the rate (Level III) equations on the water bath (control volume 1) and cooling coil (control volume 2). (b) [8 pts] When the utility fluid flow rate is very high, T2T2F. Using this assumption, determine the time required for the water bath to reach the temperature of 10C. (c) [6 pts] Most water baths are not insulated. Write the Level III model equation for a water bath that exchanges heat with the ambient air (Tair=25C). (d) [6 pts] If the surface area of the water bath (aB) is 0.27m2 and the heat transfer coefficient between the water and the ambient air (Uair) is 17W/m2K, how long will it take the water bath to reach the temperature of 10C ? (e) [8 pts] When the target temperature is reached, it is maintained constant by engaging the electrical heating element, which compensates for the further energy losses to the utility fluid. Write the Level III model equation for the water bath operating at constant temperature. (f) [4 pts] Determine the rate of electrical heat generation (Qel) required to maintain the water bath temperature at 10C