A space object has the shape of a sphere of radius R. Heat sources ensuring the heat evolution
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Answer:
When its radius is decreased by half, the temperature of the object will change by 1.19. The complete heat 'q' that is emitted by a space object per unit time is directly proportional to the volume because q = αR3, in which α is a coefficient. Now, as the amount of heat dissipated per unit area is directly proportional to T4, therefore in an equilibrium, the entire liberated heat can be lost in space. Hence, it can be written as q = βR2T4 as the surface area is directly proportional to R2. Now, when we equate the expressions for q, we get T4 = αR/β. Hence, the fourth power of the temperature of an object is directly proportional to the radius. So, a decrease in radius by half will decrease the temperature by a factor of fourth root of two, i.e., of the order or 1.19.