An ac cools the room at the rate of 4 degrees celsius per hour . What would be the temperature of the room after 6 hours, if the initial temperature of the room 42 degrees celsius.
Answers
Answer:
It won’t be a simple linear relationship as one might think. With a linear relations hip you say four dgerees per hour, 24 degrees total will take 6 hours.
But it is not that simple. The ability to cool is related to the temperature diffferential that has to be maintained.
In this case it would be reasonable to assume the room was initially at outdoor temperature of 48 C
As the initial reduction goes on, the room will cool quickly because very little cool air is lost when the first hour ends at 44 degrees to the 48 degree outside temperature based on real world wall insulation.
But as time progresses a couple of hours the temperature goes to 30 degrees, then the difference between indoors and outdoors becomes larger, some 18 C. THis means a lot of your cool will be lost when ile you are putting more in… a leaky bucket. As the bucket becomes more full the bucket leaks more.
Depending on teh capacity of the AC in BTU, at some point it will not be bale to put cool in as fast as it leaks out and the time will take forever. Even if it had positive cool flow,the losses less than input the time will take longer as the room gets cooler.
The only time that you can get a linear cool down slope in time is if the insulation is infinite, which is impossible.