1. In a batch heating vessel with an internal coil of surface area A, condensing steam at temperature Ts is used to heat a mass m of process liquid with specific heat capacity Cp. Heat is also being lost to the surroundings at temperature To through the wall of the vessel of surface area A.. The overall heat transfer coefficient from steam to process liquid is U and from process liquid to the surroundings is U.. (a) Write down an equation for the heat flow, Q, to the liquid at an instant where the liquid temperature is T. (3 marks) (b) Show that the batch heating time, t, from temperature T1 to T2 is given by EQUATION Q1.1, using EQUATION Q1.2 as help: mcp X-T in (UA+U,A.) X-T t= (+B n (7) Equation Q1.1 X= UAT, + U.A.T. UA+ U,A. Equation Q1.2 (12 marks) (c) As part of the production process of a cosmetic gel, in which the time of heating is described by the EQUATION Q1.1 and EQUATION Q1.2, a liquid mixture has to be stabilised. This is done by heating the mixture in an internal coil agitated vessel from the ambient temperature to 70C and then allowing it to "rest" (cool) at ambient temperature, without heating, for two hours. The procedure is carried out in batches of 1250 kg and the heat is provided by condensing steam with a saturation temperature of 121C. Using EQUATION Q1.1 and EQUATION Q1.2 as well as the data given in TABLE Q1, calculate the temperature at the end of the "rest" period and the total time needed for the overall process to be finished. (10 marks) TABLE Q1 Specific heat capacity of liquid mixture 2610 J kg-1 k-1 Ambient temperature 20C Surface area of internal coil 0.85 m2 Surface area of vessel wall 7.3 m2 Overall heat transfer coefficient steam-liquid 420 W m2K-1 Overall heat transfer coefficient liquid-surroundings 12 W m2K-1