question_answer

Direction: Consider a spherical body A of radius R which placed concentrically in a hollow enclosure H, of radius 4R as shown in the figure. The temperature of the body A and H are \[{{T}_{A}}\] and \[{{T}_{H}},\] respectively.

Emissivity, transitivity and reflectivity of two bodies A and H are \[\text{(}{{e}_{A}},\text{ }{{e}_{H}})\text{ (}{{t}_{A}},\text{ }{{t}_{H}}\text{)}\] and \[({{r}_{A}},\text{ }{{r}_{H}})\] respectively.

For answering following questions assume no absorption of the thermal energy by the space in-between the body and enclosure as well as outside the enclosure and all radiations to be emitted and absorbed normal to the surface.

[Take \[\sigma \times \,4\pi {{R}^{2}}\,\times \,{{300}^{4}}=\,\beta J{{s}^{-1}}\]]

The temperature of A (a perfect black body) is \[{{T}_{A}}=300K\] and temperature of H is \[{{T}_{0}}=OK\]. For H take \[{{e}_{H}}=0.5\] and \[t=0.5\]. For this situation mark out the correct statement(s).

A) The rate at which A loses the energy is \[\beta J{{s}^{-1}}\]

B) The rate at which spherical surface containing P receives the energy is \[\frac{\beta }{2}J{{s}^{-1}}\].

C) The rate at which spherical surface containing Q receives the energy is \[\beta \,J/{{s}^{-1}}\]

D) All of the above

Correct Answer: D

Solution :

[d] The diagram shows the situation clearly. The rate at which energy is emitted by A is \[\beta \,J{{s}^{-1}},\] while crossing enclosure that rate at which energy is transmitted out is \[\frac{\beta }{2},\] while remaining has been absorbed by H. So, rate at which A losses energy is \[\beta \,J{{s}^{-1}}\] and the rate at which P and Q receive energy are \[\beta /2\,J{{s}^{-1}}\] and \[\beta J{{s}^{-1}},\] respectively. This energy is received on the area of sphere passing through P and Q.