A sphere with radius 1 m has temperature 18°C. It lies inside a concentric sphere with radius 2 m and temperature 25°C. The temperature at a distance r from the common center of the spheres satisfies the differential equation below. If we let S = dT/dr, then S satisfies a first-order differential equation. Solve it to find an expression for the temperature T (r) between the spheres.

Question

Chemistry

Pokey

18 June, 12:56

A sphere with radius 1 m has temperature 18°C. It lies inside a concentric sphere with radius 2 m and temperature 25°C. The temperature at a distance r from the common center of the spheres satisfies the differential equation below. If we let S = dT/dr, then S satisfies a first-order differential equation. Solve it to find an expression for the temperature T (r) between the spheres.

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Answers (1)

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Bianca Todd · Answer 1

The expression will be T=7r

Explanation:

From equation S=dT/dr, we can solve this equation by integrating it and usig the values 25C and 18C for T and 2 and 1 for the radius. The solution to the integration will result in the value for S. For this example, it will be 7. Therefore, the main expression will be T = 7r in which the temperature is in fuction of the radius between the spheres.