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A tank contains 50 kg of water at the rate of 200 kg/h and temperature of 30° C enters the tank through an inlet pipe. A cooling coil immersed in the tank removes heat energy from water at the rate of 8 kW. A mechanical stirrer ensures through mixing of water in the tank so as to maintain a uniform temperature of water at any instant and in the process add heat energy at the rate of 0.2 kW to water. Neglecting kinetic and potential energy changes and taking the average specific heat of water as 4.2 KJ/kg-K, derive an expression for the variation of instantaneous temperature of water in the tank with respect to time.

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