Transmission Of Heat Question 349
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}} $ ] 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).
Options:
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
Show Answer
Answer:
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.
BETA
