A radiator by steam is used to heat a closed room. Heat is lost from the room to the outside at a rate of heat transfer by Newton Law. The outside temperature of the room is Tour and dimensions of room are V. Saturated steam at P, condenses in the radiator and emerges as a liquid at the saturation temperature, Ts. The temperature inside the room at the initial radiator is turned on is Tim. The overall heat transfer coefficient between inside and outside room is U. The heat capacity of air to be constant is C. Write a differential energy balance on the room air.