has radius and wall thickness as shown. The sphere is completely
sealed. The stainless steel has a density of 7.93 g/cm3, has
specific heat capacity of 500 J/(kg.K), a surface absorptivity of
0.58 and an emissivity of 0.38. It is experiencing solar radiation
of ππ ππππ = 1367 W/m2.
You may assume the following:
β’ Only radiative energy transfer is in operation externally;
β’ The temperature of the sphere is uniform throughout;
β’ There is no source of external radiative energy present besides
the sun;
β’ The sphere has an unimpeded view of space in all directions in
which to radiate.
(i) Find the steady-state temperature of the sphere assuming
that the sphere is completely empty.
(ii) Find the steady-state temperature of the sphere assuming
that the sphere contains 100 g of plutonium-238 (if you havenβt
heard of plutonium-238, I suggest you look it up β it has some
amazing properties that have made it suitable for a number of long-
duration space missions). The plutonium generates heat at a
constant rate of ππππ‘πππππ = 57 W. You do not need to estimate the
temperature of the plutonium itself here, just how the energy it
releases affects the temperature of the sphere.
(iii) Assume again that the sphere is empty but has been ejected
into space from another spacecraft at time π‘ = 0. Immediately after
it has been released, it is at a temperature π = 200 K. Find how
long it will take until the sunβs radiation raises it to a
temperature of π = 250 K.
- A Thin Walled Stainless Steel Sphere Is Shown In Figure Q 4b It Has Radius And Wall Thickness As Shown The Sphere Is C 1 (60.83 KiB) Viewed 8 times