A steam radiator is used to heat a 60-m3 room. Saturated steam at 3.0 bar condenses in the radiator and emerges as a liquid at the saturation temperature. Heat is lost from the room to the outside at a rate
where T(°C) is the room temperature and T0=0? is the outside temperature. At the moment the radiator is turned on, the temperature in the room is 10°C
a) Let Ms(kg/h) denote the rate at which steam condenses in the radiator and n(kmol) the quantity of air in the room. Write a differential energy balance on the room air, assuming that n remains constant at its initial value, and evaluate all numerical coefficients. Take the heat capacity of air (Cv) to be constant at 20.8 J/(mol?°C).
b) Write the steady-state energy balance on the room air and use it to calculate the steam condensation rate required to maintain a constant room temperature of 24°C. Without integrating the transient balance, sketch a plot of T versus t, labeling both the initial and maximum values of T
c) Integrate the transient balance to calculate the time required for the room temperature to rise by 99% of the interval from its initial value to its steady-state value, assuming that the steam condensation rate is that calculated in Part (b).
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