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process control, Chemical Engineering

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A tank contains cold water at a temperature Tc = 20°C and volume Vc = 1 m3. You add a volume Vh = 1 m3 of water at temperature Th = 100°C at time t = 0. Energy is lost from the tank mainly via conduction to the environment (which is also at Tc). (Ignore energy lost due to vaporisation) Cp = 4.2 kJ/kg°C
Propose a model (i.e. derive a Differential Equation) which will show how temperature in the tank changes with time. State assumption used. Solve this model to obtain T(t) given that T(t=200s) = 50°C.

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