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August 5th, 2012, 10:09 PM   #1
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Newton's law

The Question:
The Temperature M(t) outside a building decreases at a constant rate of 1degree per hour. The inside of the building is heated and there is no other source of cooling. The heater was switched on at time t=0, when the temperature inside, T(t), was 17 degrees and the temperature outside was 0 degrees. Assume the the heater generates a constant amount h= 50000 Btu/hr of heat when it is working, the heat capacity of the building is 1/5 degrees per thousand Btu, and the time constant for heat transfer between the outside and the inside of the building is 2hr. On the basis of Newton's law of cooling,
DT(t)/st= K(M(t)-T(t) + h
find the upper value of the temperature in the building in the time interval 0<=t<4 hr.
My problem:
I am having troubles starting this question off, the constant rate decreasing outside, is confusing me. AS well I have no idea where I am going to use the 2hr part at the end..
Please Help
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August 7th, 2012, 10:17 AM   #2
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Re: Newton's law

Quote:
Originally Posted by cynthiegaetz
The Question:
The Temperature M(t) outside a building decreases at a constant rate of 1degree per hour. The inside of the building is heated and there is no other source of cooling. The heater was switched on at time t=0, when the temperature inside, T(t), was 17 degrees and the temperature outside was 0 degrees. Assume the the heater generates a constant amount h= 50000 Btu/hr of heat when it is working, the heat capacity of the building is 1/5 degrees per thousand Btu, and the time constant for heat transfer between the outside and the inside of the building is 2hr. On the basis of Newton's law of cooling,
DT(t)/st= K(M(t)-T(t) + h
This is missing a parentheses. I think you mean DT(t)= K(M(t)- T(t))+ h.

Quote:
find the upper value of the temperature in the building in the time interval 0<=t<4 hr.
My problem:
I am having troubles starting this question off, the constant rate decreasing outside, is confusing me. AS well I have no idea where I am going to use the 2hr part at the end..
Please Help
The temperature outside was 0 degress at t= 0 and is decreasing at 1 degree per hour so if t is in hours, the temperature outside at t hours is M(t)= -t degrees.
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