A thin copper rod of uniform cross section A square metres and of length L metres has a spherical metal sphere of radius r metre at tis one end symmetrically attached to the copper rod. The thermal conductivity of copper is K and the emissivity of the spherical surface of the sphere is `epsi`.The free end of the copper rod is maintained at the temperature T kelving by supplying thermal energy from a P watt source. Steady state conditions are allowed ot be established while the rod is properly insulated aginst heat loss from its lateral surface. Surroundings are at `0^@C` Stefan's constant`=sigmaW//m^(2) K^(4)`.
The net power that will be radiated out, `P_S` from the sphere after steady state condition are reached is

Options

A. `P_S=P`
B. `P_S=(PA)/(4pir^2)`
C. `P_S=0`
D. `P_S=sigmaepsiT_S^4`

Answer

A

Explanation

Under Steady state Conditions, all temperature remain constant incuding `T_S`, the temperature at centre of sphere. Hence no thermal energy accumulates inside the sphere. Hence `P_S=P=` energy received from source.