Answer:
The outer diameter of the ball is 6.2138 cm
Explanation:
The formula to apply is ;
Heat loss ,
![Q/t=kA*\frac{( T_1-T_2)}{d}](https://tex.z-dn.net/?f=Q%2Ft%3DkA%2A%5Cfrac%7B%28%20T_1-T_2%29%7D%7Bd%7D)
where ;
Q/t=total heat loss from the ball = 1600 w
k=coefficient of heat transmission through the ball= 2.75 W/m.˚C
A=area in m² of the ball with the coefficient of heat transmission
T₁=Hot temperature
T₂=Cold temperatures
d=thickness of the ball
Area of spherical ball using internal diameter, 3cm= 0.03 m will be
Radius = half the diameter = 0.03/2 = 0.015
Area = 4 *π*r²
Area = 4*π*0.015² = 0.002827 m²
Apply the formula for heat loss to get the thickness as:
1600 = {2.75 * 0.002827 *(250-30 ) }/d
1600 =1.711/d
1600d = 1.711
d=1.711/1600 = 0.001069 m
d= 0.1069
Using internal radius and the thickness to get outer radius as;
3 + 0.1069 = 3.1069 cm
Outer diameter will be twice the outer radius
2*3.1069 = 6.2138 cm