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 \[\sigma \times \,4\pi {{R}^{2}}\,\times \,{{300}^{4}}=\,\beta J{{s}^{-1}}\]] |
A) The rate at which A loses the energy is
B) The rate at which the spherical surface containing P receives the energy is zero
C) The rate at which the spherical surface containing Q receives the energy is\[\beta \].
D) All of the above
Correct Answer: D
Solution :
[d] Now, in this case, each of incidence, reflection and absorption take place. The rate of which energy has been lost by A is, \[P=\,-\,[{{P}_{absorbed}}-\,{{P}_{emitted}}]\] \[=-\,\left[ \frac{\beta }{8}+\,\frac{\beta }{32}+\,..... \right]\,+\,\left[ \frac{\beta }{2}\,+\frac{\beta }{8}+\,\frac{\beta }{32}+\,.... \right]\,=\,\frac{\beta }{2}\] The rate at which energy is received by P is, \[{{P}_{1}}=0\] The rate at which energy is received by Q is, \[{{P}_{2}}=\,\left( \frac{\beta }{2}+\,\frac{\beta }{8}+\,... \right)\,+\,\left( \frac{\beta }{4}+\,\frac{\beta }{16}+.. \right)\] \[=\,\frac{\beta }{2}\,\times \,\frac{4}{3}+\,\frac{\beta }{4}\,\,\times \,\frac{4}{3}=\beta \]You need to login to perform this action.
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