CBEE 212Written HW 8Winter 2015Ë†A steam radiator is used to heat a room. Saturated steam at 3 bar (with specific enthalpy H1 )Ë†condenses in the radiator and emerges as a saturated liquid at 1 bar (with specific enthalpy H 2 ). Heatis lost from the room to the surroundings at a rate: Qlost = h(T â€“ T2), where T is the temperature of theair inside the room, h = 0.02 kW/Â°C is a heat transfer coefficient and T2 = 0Â°C is the temperatureoutside the room. You may assume that the amount of air in the room remains constant at n = 5000moles and that the heat capacity of the air is constant at Cv = 0.021 kJ/mol∙Â°C.a. Write a differential energy balance on the air in the room. Use only symbolic variables (i.e., nonumbers). Use m for the mass flow rate of steam to the radiator.Ë† Ë†b. Solve for the steady-state temperature (Ts) in terms of h, H1 , H 2 , and m . Determine the requiredmass feed rate of the steam to the radiator to achieve a steady-state temperature of 24Â°C in theroom air.c. The radiator is turned on when the room air temperature is 10Â°C. Determine the time required toreach T = 23Â°C. Use the same mass feed rate as calculated in part b (i.e., for Ts = 24Â°C). Hint:the math will be simpler if you substitute the algebraic equation for Ts into the differential energybalance equation, and then integrate.
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