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

Byju's Answer

Standard VII

Physics

Conduction

Two blocks of...

Question

Two blocks of the same thickness and thermal conductivities $k_{1} a n d k_{2}$ are placed in contact. Their outer surfaces are kept at constant temperatures $T_{1} a n d T_{2}$ . If $T_{2}$ > $T_{1}$ , and $k_{2}$ > $k_{1}$ the temperature of the interfaces in the steady state will be

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

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

Open in App

Solution

The correct option is A

Let T be the temperature of the interface in the steady state and let d be the thickness of each block. Now, insteady state, the rate of flow of heat through each block must be the same, i.e.

$\frac{k_{1} A (T_{1} - T)}{d} = \frac{k_{2} A (T - T_{2})}{d} o r k_{1} (T_{1} - T) = k_{2} (T - T_{2})$

Which give $T = \frac{k_{1} T_{1} + k_{2} T_{2}}{k_{1} + k_{2}}$ , which is choice (a)

Suggest Corrections

Similar questions

Q. Two bars of same length and same cross-sectional area but of different thermal conductivities

K_{1}

and

K_{2}

are joined end to end as shown in the figure. One end of the compound bar is at temperature

T_{1}

and the opposite end at temperature

T_{2}

(where

T_{1} > T_{2}

).The temperature of the junction is

Q. Two walls of thickness

d_{1}

and

d_{2}

, thermal conductivities

K_{1}

and

K_{2}

are in contact. In the steady state, if the temperature at the outer surfaces are

T_{1}

and

T_{2}

, the temperature at the contact of the walls will be

Q. Two walls of thickness

d_{1}

and

d_{2}

, thermal conductivities

K_{1}

and

K_{2}

are in contact. In the steady state if the temperature at the outer surfaces are

T_{1}

and

T_{2}

, the temperature are the common wall will be

Q. Two walls of thickness

d_{1}

and

d_{2}

thermal conductivities

K_{1}

and

K_{2}

are in contact. In the steady state if the temperatures at the outer surfaces are

T_{1}

and

T_{2},

the temperature at the common wall will be

Two plates of the same area and the same thickness having thermal conductivities $k_{1}$ and $k_{2}$ are placed one on top of the other. The top and bottom faces of the composite plate are maintained at different constant temperatures. The thermal conductivity of the composite plate will be

Join BYJU'S Learning Program

Two blocks of the same thickness and thermal conductivities k1 and k2 are placed in contact. Their outer surfaces are kept at constant temperatures T1 and T2. If T2 > T1, and k2 > k1 the temperature of the interfaces in the steady state will be

Two blocks of the same thickness and thermal conductivities $k_{1} a n d k_{2}$ are placed in contact. Their outer surfaces are kept at constant temperatures $T_{1} a n d T_{2}$ . If $T_{2}$ > $T_{1}$ , and $k_{2}$ > $k_{1}$ the temperature of the interfaces in the steady state will be