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Set 54 Problem number 10


Problem

A wall has area 11 m^2 and constant thickness .24 m.   The inside of the wall is at 193 Celsius while the outside is at 3 Celsius.   What is the temperature gradient from inside to outside?

If the outside temperature increased, thereby increasing the temperature difference by a factor of 1.254, what would be the temperature gradient?

Solution

The temperature changes by -190 Celsius through the .24 m thickness of the wall. The average temperature gradient (which is the temperature change per unit of distance) is therefore

If the temperature difference increases by factor 1.254, the temperature gradient, which is proportional to the temperature difference, will change by the same factor. Thus the new temperature gradient will be

Generalized Solution

The average temperature gradient is the average temperature change per unit of distance:

If the thickness of a wall is `dx and the inside and outside temperatures of the wall surface are T2 and T1, then `dT = T2 - T1 and

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