Question

Select One Correct Option from the following : 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 large thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T, respectively. The temperature of the middle (i.e. second) plate under steady state condition is
(A) $(\frac{65}{2}) ^{1/4} T$
(B) $(\frac{97}{4}) ^{1/4} T$
(C) $(\frac{97}{2} )^{1/4} T$
(D) $(97)^{1/4} T$.

Answer 1

According to Stefan−Boltzmann law of rate of radiant  energy emmission per unit area of a body is given by,R=ε σ T4,   where εis emmissivity, σ Stefan's constant and T the temperature of the body.In case the body is a black body then ε=1, thus for black body the formula is modified as,R= σ T4.  At steady state condition,heat energy absorbed= heat energu radiated.heat energy absorbed=σ(3T)4+σ(2T)4=σ(81+16)T4=σ ×97 T4. heat energu radiated=σ×2 T40.   Now applying condition for steady state,σ×2 T40=σ ×97 T4     or       T40=972  T4    OR    T0=(972)14T.Thus (c) (972)14T is the right answer.

Answer 2

please refer to the attached photo