Please consider a classroom that is 55 x 35 x 9 with a full

Please consider a classroom that is 55” x 35” x 9” with a full occupancy of 70 persons. The classroom is located in the southwest corner of a building and has two exterior walls and with 6 windows (3’ x 4’ with a single pane of glass). During hot months, the thermostat in the classroom is programed to power up the AC unit when the temperature reaches 78 degrees F (max temperature) and then power off the AC unit when the classroom air has been cooled to 72 degrees F (min temperature). The AC unit is rated at 4.0 tons. Data on an average occupant:

Age: 20.6 yrs. Volume: 2.5 ft^3 Mass: 156.40 lbm Heat emission: 450 Btu/hr (all heat transfer modes combined) Height: 5\' 9.2\"

Data on air: Diatomic Ideal Gas behaving ideally, Pressure = 30.05 in Hgo (Physical properties well represented by the Ideal Gas Law at the mean of the min and max temperatures.) Molecular Mass = 29.96 amu

We will now model the time required for one cooling cycle under the assumption that the occupants are the sole source of heat in the classroom.

a. Can one reasonably assume that the total volume of the occupants is negligible? Why or why not?

b. How long (in min) is required for the classroom to warm from the min to the max temperature when fully occupied. How long (in min) is required for the classroom (when fully occupied) to cool from the max to the min temperature (in min)? What is the total time for the cycle (in min)? We will now work under the more realistic assumption that there are sources of heat in addition to the occupants.

c. In addition to the occupants, what sources of heat exist in a classroom that is similar to our Thermo classroom (450 EN)? Please list at least three.

d. Let the additional heat sources be described by the expression Q [Btu hr ] = 5,500 + 375(t 72) where t = the external air temperature in degrees F. What is the greatest external air temperature (in degrees F) that allows the AC unit to cycle instead of operating in a continuous mode?

Solution

Can one reasonably assume that the total volume of the occupants is negligible? Why or why not?

b. How long (in min) is required for the classroom to warm from the min to the max temperature when fully occupied. How long (in min) is required for the classroom (when fully occupied) to cool from the max to the min temperature (in min)? What is the total time for the cycle (in min)? We will now work under the more realistic assumption that there are sources of heat in addition to the occupants.

c. In addition to the occupants, what sources of heat exist in a classroom that is similar to our Thermo classroom (450 EN)? Please list at least three.

d. Let the additional heat sources be described by the expression Q [Btu hr ] = 5,500 + 375(t 72) where t = the external air temperature in degrees F. What is the greatest external air temperature (in degrees F) that allows the AC unit to cycle instead of operating in a continuous mode?