CBEE 212Written HW 8Winter 2015Ë?A steam radiator is used to heat a room. Saturated steam at 3 bar (

CBEE 212Written HW 8Winter 2015ˆA steam radiator is used to heat a room. Saturated steam at 3 bar (with specific enthalpy H1 )ˆcondenses 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 – T2), where T is the temperature of theair inside the room, h = 0.02 kW/°C is a heat transfer coefficient and T2 = 0°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∙°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.ˆ ˆb. 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 24°C in theroom air.c. The radiator is turned on when the room air temperature is 10°C. Determine the time required toreach T = 23°C. Use the same mass feed rate as calculated in part b (i.e., for Ts = 24°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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