Question

The variation of the temperature in a plane wall is determined to be T ( x ) = 110 − 60 x where x is in m and T is in degree Celsius. If the thickness of the wall is 0.75 m, the temperature difference between the inner and outer surfaces of the wall is

A. 60 C
B. 84 C
C. 30 C
D. 45 C
E. 75 C

Answer 1

The temperature difference between the inner and outer surfaces of the wall, based on the given temperature distribution T(x) = 110 - 60x, is 45°C.

Step-by-step explanation:

To find the temperature difference between the inner and outer surfaces of the wall given the temperature distribution T(x) = 110 - 60x, we need to calculate the temperatures at the two surfaces. The inner surface is at x = 0 and the outer surface is at x = the thickness of the wall, which is given as 0.75 m.

At the inner surface (x = 0):
T(0) = 110 - 60(0)
T(0) = 110°C

At the outer surface (x = 0.75):
T(0.75) = 110 - 60(0.75)
T(0.75) = 110 - 45
T(0.75) = 65°C

Now, the temperature difference ΔT between the inner and outer surfaces is:
ΔT = T(0) - T(0.75)
ΔT = 110°C - 65°C
ΔT = 45°C

Therefore, the correct answer is D. 45 C.