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

Preparation of Hydrogen

One end of a ...

Question

One end of a thermally insulated rod is kept at a temperature $T$ $_{1}$ and the other at $T_{2}$ . The rod is composed of two sections of lengths $l_{1}$ and $l_{2}$ and thermal conductivities $k_{1}$ and $k_{2}$ respectively as shown in the figure. The temperature at the interface of the two sections is :

\frac{(k_{2} l_{2} T_{1} + k_{1} l_{1} T_{2})}{(k_{1} l_{1} + k_{2} l_{2})}

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

\frac{(k_{2} l_{1} T_{1} + k_{1} l_{2} T_{2})}{(k_{2} l_{1} + k_{1} l_{2})}

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

\frac{(k_{1} l_{2} T_{1} + k_{2} l_{1} T_{2})}{(k_{1} l_{2} + k_{2} l_{1})}

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

\frac{(k_{1} l_{1} T_{1} + k_{2} l_{2} T_{2})}{(k_{1} l_{1} + k_{2} l_{2})}

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

Open in App

Solution

The correct option is B $\frac{(k_{1} l_{2} T_{1} + k_{2} l_{1} T_{2})}{(k_{1} l_{2} + k_{2} l_{1})}$
$\frac{Q_{1}}{t} = \frac{(T_{1} - T) k_{1}}{l_{1}} A$

$\frac{Q_{2}}{t} = \frac{(T - T_{2}) k_{2}}{l_{2}} A$

$\frac{Q_{1}}{t} = \frac{Q_{2}}{t}$

$(T_{1} - T) k_{1} l_{2} = (T - T_{2}) k_{2} l_{1}$

$T = \frac{k_{1} l_{2} T_{1} + k_{2} l_{1} T_{2}}{k_{1} l_{2} + k_{2} l_{1}}$

Suggest Corrections

Similar questions

Q. One end of a thermally insulated rod is kept at a temperature

T_{1}

and the other at

T_{2}

. The rod is composed of two sections of lengths

l_{1}

and

l_{2}

and thermal conductivities

k_{1}

and

k_{2}

respectively. The temperature at the interface of the two sections is:

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 rods

P

and

Q

have equal lengths. Their thermal conductivities are

K_{1}

and

K_{2}

and cross-sectional areas are

A_{1}

and

A_{2}

. When the temperature at ends of each rod are

T_{1}

and

T_{2}

respectively, the rate of flow of heat through

P

and

Q

will be equal, if

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

Q. Two walls of thickness

l_{1}

and

l_{2}

and thermal conductivities

k_{1}

and

k_{2}

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

T_{1}

and

T_{2}

, the temperature at the common wall is :

Join BYJU'S Learning Program

One end of a thermally insulated rod is kept at a temperature T1 and the other at T2. The rod is composed of two sections of lengths l1 and l2 and thermal conductivities k1 and k2 respectively as shown in the figure. The temperature at the interface of the two sections is :

The correct option is B (k1l2T1+k2l1T2)(k1l2+k2l1)Q1t=(T1−T)k1l1AQ2t=(T−T2)k2l2AQ1t=Q2t(T1−T)k1l2=(T−T2)k2l1T=k1l2T1+k2l1T2k1l2+k2l1