Assuming steady state one-dimensional heat conduction in a composite slab- if Tinter - T1-T22- then which of the following statements is true about the respective thermal conductivities-

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Physics

Conduction Law

Assuming stea...

Question

Assuming steady state one-dimensional heat conduction in a composite slab, if $T_{i n t e r} = \frac{T_{1} + T_{2}}{2},$ then which of the following statements is true about the respective thermal conductivities?

2 K_{1} = K_{2}

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

K_{1} = K_{2}

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

2 K_{1} = 3 K_{2}

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

K_{1} = 2 K_{2}

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

Open in App

Solution

The correct option is D $K_{1} = 2 K_{2}$
Given, $T_{i n t e r} = \frac{T_{1} + T_{2}}{2}$
As heat flow throughout the slabs is same [steady state],
$Q_{1} = Q_{2} . . . . . . . (1)$
Rate of heat flow in slab -1 : $Q_{1} = K_{1} A \frac{(T_{1} - \frac{T_{1} + T_{2}}{2})}{2 b} = K_{1} A \frac{T_{1} - T_{2}}{4 b}$
Similarly:
$Q_{2} = K_{2} A \frac{(\frac{T_{1} + T_{2}}{2} - T_{2})}{b} = K_{2} A \frac{T_{1} - T_{2}}{2 b}$
[Area $A$ is the same]
From $(1)$ , we get
$\frac{K_{1}}{2} (\frac{T_{1} - T_{2}}{2}) = K_{2} (\frac{T_{1} - T_{2}}{2})$
$\Rightarrow \frac{K_{1}}{2} = K_{2}$ or $K_{1} = 2 K_{2}$
Thus, option (d) is the correct answer.

Suggest Corrections

Similar questions

Q. Assuming steady state one-dimensional heat conduction in a composite slab, if

T_{i n t e r} = \frac{T_{1} + T_{2}}{2},

then which of the following statements is true about the respective thermal conductivities?

Q. The temperature variation under steady heat conduction across a composite slab of two materials with thermal conductivities

K_{1}

and

K_{2}

is shown in figure. Then, which one of the following statements holds?

Q. The temperatures of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivities K and 2K and thicknesses, x and 4x respectively are

T_{2} a n d T_{1} w i t h T_{2} > T_{1}

. The rate of heat transfer through the slab, in a steady state is

\frac{k A (T_{2} - T_{1})}{x} α

What is the value of

α

The temperature of the two outer surfaces of a composite slab consisting of two materials having coeffieient of thermal conductivity

K

and

2 K

and thickness

x

and

4 x

respectively are

T_{2}

and

T_{1}

(

T_{2} > T_{1}

). The rate of heat transfer through the slab, in a steady state is

(\frac{A (T_{2} - T_{1}) K}{x}) f

with f equal to

The temperatures of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are $T_{2}$ and $T_{1}$ ( $T_{2} > T_{1}$ ). The rate of heat transfer through the slab, in a steady state is $(\frac{A (T_{2} - T_{1}) K}{x}) f$ , with f equal to

Join BYJU'S Learning Program

Explore more

Conduction Law

Standard XIII Physics

Join BYJU'S Learning Program

Assuming steady state one-dimensional heat conduction in a composite slab, if Tinter=T1+T22, then which of the following statements is true about the respective thermal conductivities?

Assuming steady state one-dimensional heat conduction in a composite slab, if $T_{i n t e r} = \frac{T_{1} + T_{2}}{2},$ then which of the following statements is true about the respective thermal conductivities?