Question

Q : It is desired to maintain the temperature of hospital room at 24 degree centigrade at all the time . The size of the room is 12x12 having 2 ton Air conditioner and 1200 watt heater.

A) discuss proper mechanism so that the temperature should not exceed 24 degree centigrade at any condition ( Hot or cold weather ).

B) suggest and draw a block diagram for temperature control system for hospital room

Answer 1

Ton in si units is 3.5 kW. I.e., the AC can remove heat energy at a maximum rate of 3.5 kW = 3500 W

The heater is rated at 1200 W.

So, in order to ensure that the room is kept at at temperature T (say), we need to ensure that

1) during summer (hot weather), the influx of heat energy less than 3500 W.

2) during winter, the outflux of heat energy should be less than 1200 W.

The above conditions can be met with insulation. SO, it is necessary to have insulation that will certainly prevent the flow of heat outside more than 1200 W and inflow of heat energy greater than 3500 W.

Reflecting glass during summer and wooden flooring for winter are options.

The size of the room is given as 12x12. I will assume that it is in feet. I will also assume that the height of the room is also 12 foot such that the volume of the entire room is 12x12x12 ft^3 = 1728 ft^3 = 48.93 m^3

Assume that the room is only containing air. At a room temperature of 24 deg cent, the density of air is 1.18 kg/m^3.

So, the total air inside is: m= density* volume = 57.74 kg

A thermostat is required to detect a temperature fluctuation in the room. If the temperature even fluctues to 24-0.06 =24.006 deg cel , the air conditioner has to start working.

0.006 deg cel was arrived in this manner: The heat capacity of air at 24 deg C is 1000 J/kg. So, the total heat capacity of the room is C=c*m = 1000 J/kg.K * 57.74 kg = 57740 J/K

Now, if the temperature is 24.06 deg C, the heat that has been gained is 0.06*57740J/K = 3464.4 J. SO, in order to remove it in one second ( I have set the critical time as 1 second) , the AC already has to work in full power! (Since it can remove at most 3500 Joules per second)

A similar explanation can also be attained for the winter season and the heater.

Here is a block diagram for the temperature control.