Heat and Thermodynamics 3 Question 9
9. 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
(2012)
(a) $\left(\frac{65}{2}\right)^{\frac{1}{4}} T$
(b) $\left(\frac{97}{4}\right)^{\frac{1}{4}} T$
(c) $\left(\frac{97}{2}\right)^{\frac{1}{4}} T$
(d) $(97)^{\frac{1}{4}} T$
Show Answer
Solution:
- Let temperature of middle plate in steady state is $T _0$
$$ Q _1=Q _2 $$
$Q=$ net rate of heat flow
$\therefore \quad \sigma A(3 T)^{4}-\sigma A T _0^{4}=\sigma A T _0^{4}-\sigma A(2 T)^{4}$
Solving this equation, we get
$$ T _0=\left(\frac{97}{2}\right)^{1 / 4} T $$
