Three very large plates of same area are kept parallel and close to each other. They are considered

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10-2.Transmission of Heat

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Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2\,T$ and $3\,T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is

${\left( {\frac{{65}}{2}} \right)^{\frac{1}{4}}}\,T$

${\left( {\frac{{97}}{4}} \right)^{\frac{1}{4}}}\,T$

${\left( {\frac{{97}}{2}} \right)^{\frac{1}{4}}}\,T$

${\left( {97} \right)^{\frac{1}{4}}}\,T$

Solution

In steady state energy absorbed by middle plate is equal to energy released by middle plate. $\sigma \mathrm{A}(3 \mathrm{T})^{4}-\sigma \mathrm{A}\left(\mathrm{T}^{\prime}\right)^{4}=\sigma \mathrm{A}\left(\mathrm{T}^{\prime}\right)^{4}-\sigma \mathrm{A}(2 \mathrm{T})^{4}$

$(3 \mathrm{T})^{4}-\left(\mathrm{T}^{\prime}\right)^{4}=\left(\mathrm{T}^{\prime}\right)^{4}-(2 \mathrm{T})^{4}$

$2\left(\mathrm{T}^{\prime}\right)^{4}=(16+81) \mathrm{T}^{4}$

$\mathrm{T}^{\prime}=\left(\frac{97}{2}\right)^{\frac{1}{4}} \mathrm{T}$

Standard 11

Physics

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Solution

Similar Questions

The radiant energy from sun incident normally at the surface of earth is $20\, k\,cal/m^2- min$. What would have been the radiant energy incident normally on the earth if the sun had a temp. twice of the present one ? ……….. $k\,cal/m^2- min$

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