One end of a thermally insulated rod is kept at a temperature T1 and other at T2 . The rod is composed of two sections of lengths l1 and l2 and thermal conductivities K1 and K2 respectively. The temperature at the interface of the two sections is

Question

One end of a thermally insulated rod is kept at a temperature T1 and other at T2 . The rod is composed of two sections of lengths l1 and l2 and thermal conductivities K1 and K2 respectively. The temperature at the interface of the two sections is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-ap7be8gsaftv4e0w.jpg" /> (A) (((. K)2 l2 T1 + K1 l1 T2 .)/(. K1 l1 + K2 l2 .)) (B) (((. K)2l1T1+K1l2T2.)/(. K2 l1 + K1 l2 .)) (C) (((. K)1l2T1+K2l1T2.)/(. K1 l2 + K2 l1 .)) (D) (((. K)1l1T1+K2l2T2.)/(. K1 l1 + K2 l2 .))

Tardigrade Admin · Accepted Answer

Let temperature at the interface is T . For part AB , <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-ap7be8gsaftvopac.jpg" /> (Q1/t) propto ((T1 - T) K1/l1) For part BC , (Q2/t) propto ((T - T2) K2/l2) At equilibrium, (Q1/t)=(Q2/t) ∴ ((T1 - T) K1/l1)=((T - T2) K2/l2) ⇒ T=(T1 K1 l2 + T2 K2 l1/K1 l2 + K2 l1)

Q. One end of a thermally insulated rod is kept at a temperature $T_{1}$ and 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

$\frac{( ( K ) _{2} l _{2} T _{1} + K _{1} l _{1} T _{2} )}{( K _{1} l _{1} + K _{2} l _{2} )}$

$\frac{( ( K ) _{2} l _{1} T _{1} + K _{1} l _{2} T _{2} )}{( K _{2} l _{1} + K _{1} l _{2} )}$

$\frac{( ( K ) _{1} l _{2} T _{1} + K _{2} l _{1} T _{2} )}{( K _{1} l _{2} + K _{2} l _{1} )}$

$\frac{( ( K ) _{1} l _{1} T _{1} + K _{2} l _{2} T _{2} )}{( K _{1} l _{1} + K _{2} l _{2} )}$

Q. One end of a thermally insulated rod is kept at a temperature T1​ and other at T2​ . The rod is composed of two sections of lengths l1​ and l2​ and thermal conductivities K1​ and K2​ respectively. The temperature at the interface of the two sections is

(K1​l1​+K2​l2​)((K)2​l2​T1​+K1​l1​T2​)​

(K2​l1​+K1​l2​)((K)2​l1​T1​+K1​l2​T2​)​

(K1​l2​+K2​l1​)((K)1​l2​T1​+K2​l1​T2​)​

(K1​l1​+K2​l2​)((K)1​l1​T1​+K2​l2​T2​)​

Let temperature at the interface is T . For part AB , tQ1​​∝l1​(T1​−T)K1​​ For part BC , tQ2​​∝l2​(T−T2​)K2​​ At equilibrium, tQ1​​=tQ2​​ ∴ l1​(T1​−T)K1​​=l2​(T−T2​)K2​​ ⇒ T=K1​l2​+K2​l1​T1​K1​l2​+T2​K2​l1​​

Q. One end of a thermally insulated rod is kept at a temperature $T_{1}$ and 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

$\frac{( ( K ) _{2} l _{2} T _{1} + K _{1} l _{1} T _{2} )}{( K _{1} l _{1} + K _{2} l _{2} )}$

$\frac{( ( K ) _{2} l _{1} T _{1} + K _{1} l _{2} T _{2} )}{( K _{2} l _{1} + K _{1} l _{2} )}$

$\frac{( ( K ) _{1} l _{2} T _{1} + K _{2} l _{1} T _{2} )}{( K _{1} l _{2} + K _{2} l _{1} )}$

$\frac{( ( K ) _{1} l _{1} T _{1} + K _{2} l _{2} T _{2} )}{( K _{1} l _{1} + K _{2} l _{2} )}$