If the system is defined as all of the contents of the room, adding furniture will increase the total mass of the system. This will have to be accounted for in the energy balance. Starting from equation 3.32 when only the air is in the room;

      Eq 3.32

This modified term will then appear in the numerator of the time constant, causing an increase in its value.

The increase of the time constant will result in a slower response. The general slope of the heating curve will be reduced. This makes sense due to the fact that the load placed on the heating system has been increased.

By insulating the room, the overall heat transfer coefficient would be affected. This term, originally at 45x10³ cal/(°C hr) would be lowered.   If we were to draw on our intuition, we should be able to envision the effect of insulation on the process reaction curve.  The insulated room would warm up faster, and cool down more slowly, both due to a lower amount of heat loss to the exterior.   Our model supports this.

First consider the room as it cools.  With the change in UA, the time constant has increased.

This increase in the time constant will result in a more gradual cooling curve, ending at the exterior temperature of 10°C.  This is as we would expect.

Secondly, consider the room as it is heated.  As the furnace is heating the room, we must first determine what the final temperature would be under the new insulated conditions.  Since the room will experience a lower heat loss to the exterior, we will expect the final temperature to be higher than the initial case.  If one were to assume that UA was reduced by 50%, the new final temperature would be 76.6°C, up from 43.3°C. This calculation was performed using the method  provided in Example 3.4.

Since the system is striving to ultimately reach a higher temperature, the initial slope, of the increasing room temperature, would be steeper than the initial case.