CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Stefan-Boltzman's Law

Three very la...

Question

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?

A

{(\frac{65}{2})}^{1 / 4} T

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

{(\frac{97}{4})}^{1 / 4} T

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

{(\frac{97}{2})}^{1 / 4} T

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

(97)^{1 / 4} T

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C ${(\frac{97}{2})}^{1 / 4} T$
The net heat received by the middle plate from the hotter plate is equal to the net heat given to the cooler plate. Hence
$σ A ({(3 T)}^{4} - T_{o}^{4}) = σ A (T_{o}^{4} - {(2 T)}^{4})$
or
$T_{o}^{4} = \frac{97 T^{4}}{2} \Rightarrow T_{o} = {(\frac{97}{2})}^{\frac{1}{4}} T$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Three very large plates of same area 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 temperature

2 T

3 T

respectively. The temperature of the middle (i.e. sound) plate under steady state condition is
(correct answer + 1, wrong answer - 0.25)

Q. 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 of 2T and 3T respectively. The temperatures of the middle (i.e. second) plate under steady state condition is then

Q. Two large black plane surfaces are maintained at constant temperatures

T_{1}

T_{2} (T_{1} > T_{2})

. Two thin black plates

A

B

are placed between the two surfaces and in parallel to the given plates. After some time, steady conditions are obtained. By what factor, is the steady heat flow increased due to the removal of black plates?

Q. Three large conducting parallel plates each having same area are connected to a battery.

E_{1}

is the energy stored between the plates initially and

E_{2}

F_{1}

is the force between plates 1 and 3 initially and

F_{2}

is the force between them finally.
Match List

I

I I

and select the correct answer using the codes given below the lists.

	List $I$	List $I I$
p.	Now, the middle plate shifts towards the third plate very slowly keeping $1^{s t}$ and $3^{r d}$ plates fixed. Initial and final situations shown in figure. Then	1. $\frac{E_{1}}{E_{2}} > 1$
q.	Three large conducting parallel plates each having same area are connected to the battery and the space between the $2^{n d}$ and $3^{r d}$ plates is filled with dielectric. Now, the dielectric is removed very slowly. Then	2. $\frac{E_{1}}{E_{2}} < 1$
r.	Three large conducting parallel plates each having same area and having charges $- Q$ , $2 Q$ and $- Q$ respectively initially. Now first plate shifts towards the left and $3^{r d}$ towards right keeping $2^{n d}$ fixed. Then	3. $\frac{F_{1}}{F_{2}} < 1$
s.	Three large conducting parallel plates each having same area, charge on $1^{s t}$ plate is $-$ $Q$ , on $2^{n d}$ plate is $Q$ and the third is uncharged. Now, the switch is closed. If $F_{1}$ is the force between plate 1 and 3 initially and $F_{2}$ is the force between them finally, then	4. $\frac{F_{1}}{F_{2}} = 1$

Q. Three large identical conducting plates of area

A

are closely placed parallel to each other as shown (the area

A

is perpendicular to plane of diagram). The net charge on left, middle and right plates are

Q_{L}, Q_{M}

Q_{R}

respectively. If three infinitely large parallel surfaces

S_{L}, S_{M}

S_{R}

are drawn passing through middle of each plate such that surfaces are perpendicular to plane of diagram as shown, then choose the correct option (s).

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Laws of Radiation

PHYSICS

Watch in App

explore_more_icon

Explore more

Stefan-Boltzman's Law

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon