Transmission Of Heat Question 350
Question: 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},e _{H})\text{ (}t _{A},t _{H}\text{)} $ and $ (r _{A},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}} $ ] In above question, if body A has $ e _{A}=0.5, $ $ r _{A}=0.5 $ and for H, $ e _{H}=0.5, $ $ r=0.5, $ then mark out the correct statement.
Options:
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
Show Answer
Answer:
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}] $
$ =-,[ \frac{\beta }{8}+,\frac{\beta }{32}+,….. ],+,[ \frac{\beta }{2},+\frac{\beta }{8}+,\frac{\beta }{32}+,…. ],=,\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}=,( \frac{\beta }{2}+,\frac{\beta }{8}+,… ),+,( \frac{\beta }{4}+,\frac{\beta }{16}+.. ) $
$ =,\frac{\beta }{2},\times ,\frac{4}{3}+,\frac{\beta }{4},,\times ,\frac{4}{3}=\beta $
BETA
