We would like to have a simple model to describe how temperature changes with time in...

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Mechanical Engineering

We would like to have a simple model to describe how temperaturechanges with time in your classroom during lecture in a typical dayin Fall and Spring. You can consider two sets of average airtemperature – one in October and other one in April for youranalysis. Also, for simplicity, consider the entire room to be atone temperature T. Outside air (Ti,) comes in and reaches thetemperature of the room through mixing, and this air leaves at thesame rate (?). Consider all the possible modes of heat transferthat can take place through the walls (wall resistance), doors,windows (double pane vs single pane), insulation, and as well asmetabolic heat generated by us (typically about 60 W per person).Perform an energy balance for the room from which you can calculatethe room temperature, T. You need to account for air properties(density of 1.1769 kg/m3and specific heat of 1006 J/kg.K), room,window, and door dimensions. Consider an average air velocitythrough the doors as 0.1 m/s needed to calculate air flow rate ?.Ignore temperature variation in the air properties in the room.Assume reasonable parameter values needed for numericalcalculations. Our goal is to calculate the classroom temperature atthe end of a 75 minute lecture? Also makes some observationsbetween cost and energy savings if you plan to incorporate anyimprovements.

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