Three large identical plates are kept paralle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Since the plates do not touch each other, heat exchange occurs through radiation.In a steady state, the heat gained by the middle plate must equal

Vedclass · Accepted Answer

$1.7$

Vedclass · Answer

(C) Since the plates do not touch each other, heat exchange occurs through radiation.In a steady state, the heat gained by the middle plate must equal the heat lost by it.Let $A$ be the area of each plate, $\varepsilon$ be the emissivity, and $\sigma$ be the Stefan-Boltzmann constant. Let $T_1$ be the temperature of the middle plate.The heat received by the middle plate from the outer plates is $Q_{in} = A \varepsilon \sigma T^4 + A \varepsilon \sigma (2T)^4$.The middle plate emits radiation from both of its surfaces, so the heat lost is $Q_{out} = 2 A \varepsilon \sigma T_1^4$.Equating $Q_{in} = Q_{out}$:$A \varepsilon \sigma T^4 + A \varepsilon \sigma (16T^4) = 2 A \varepsilon \sigma T_1^4$$17 T^4 = 2 T_1^4$$T_1^4 = \frac{17}{2} T^4 = 8.5 T^4$$T_1 = (8.5)^{1/4} T \approx 1.71 T$.Thus, the temperature is close to $1.7 T$.

Three large identical plates are kept parallel to each other. The outer two plates are maintained at temperatures $T$ and $2T$, respectively. The temperature of the middle plate in steady state will be close to ........... $T$.

Similar Questions

The rate of radiation by a black body is $R$ at temperature $T$. Another body has the same area but an emissivity of $0.2$ and a temperature of $3T$. Its rate of radiation is:

$A$ sphere and a cube,both made of copper,have equal volumes and are black. They are allowed to cool at the same temperature and in the same atmosphere. The ratio of their rate of loss of heat is:

$A$ black body radiates at the rate of $W$ watts at a temperature $T$. If the temperature of the body is reduced to $T/3$,it will radiate at the rate of (in Watts):

The adjoining diagram shows the spectral energy density distribution $E_\lambda$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ......... $K$. (in $,000$)

$A$ black body is at $727^\circ C$. It emits energy at a rate which is proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module