Question

Radioactive wastes are temporarily stored in a spherical container, the center of which is buried a distance of 10 m below the earth’s air-soil surface. The outside diameter of the container is 2.2 m, and 500 W of heat are released as a result of radioactive decay. If the soil surface temperature is 15°C, what is the outside surface temperature of the container?

Answer 1

Answer: 76.3 ° C

Step-by-step explanation:

Outside Distance = 10 m

Outside diameter, d = 2.2 m

R=D/2 = 2.2/2= 1.1 m

inner radius, Rs = = 1.1 m

Surface Temperature Ts = 20°C

Given that the thermal conductivity of soil, K = 0.52 W/mK

We can find the outside temperature of the container by finding the thermal temperature of conductor, T, and then summing up with the surface temperature

That is (T + Ts)

we know amount of heat, Q is given by :

Q = [(T-Ts) / (R- Rs)/4πKRRs

500 = T-20 [4π×0.52×1.1×10] / (10-1.1)

500= T-20 (71.88/8.9)

500 = T-20 (8.08)

500 = 8.08T - 161.6

8.08T = 500 + 161.6

8.08T = 661.6

T = 76.33 ° C