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One end of thermally insulated rod is ke...

One end of thermally insulated rod is kept at a temperature `T_(1)` and the other at `T_(2)`. The rod is composed of two section of length `l_(1)` and `l_(2)` thermal conductivities `k_(1)` and `k_(2)` respectively. The temerature at the interface of two section is

A

`((k_(1)l_(1)T_(1)+K_(2)l_(2)T_(2)))/((K_(1)l_(1)+K_(2)l_(2)))`

B

`((K_(2)l_(2)T_(1)+K_(1)l_(1)T_(2)))/((K_(1)l_(1)+K_(2)l_(2)))`

C

`((K_(2)l_(1)T_(1)+K_(1)l_(2)T_(2)))/((K_(2)l_(2)+K_(1)l_(2)))`

D

`((K_(1)l_(2)T_(1)+K_(2)l_(2)T_(2)))/((K_(1)l_(2)+K_(2)l_(1)))`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • 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 length l_1 and l_2 and thermal conductivities K_1 and K_2 respectively. The temperature at the interface of the two section is

    A
    `(K_1l_1T_1+K_2l_2T_2)/(K_1l_1+K_2l_2)`
    B
    `(K_2l_2T_1+K_1l_1T_2)/(K_1l_1+K_2l_2)`
    C
    `(K_2l_1T_1+K_1l_2T_2)/(K_2l_1+K_1l_2)`
    D
    `(K_1l_2T_1+K_2l_1T_2)/(K_1l_2+K_2l_1)`

  • Two rods of the same length and diameter, having thermal conductivities K_(1) and K_(2) , are joined in parallel. The equivalent thermal conductivity to the combinationk is

    A
    `(K_(1) K_(2))/(K_(1) + K_(2))`
    B
    `K_(1) K_(2)`
    C
    `(K_(1) + K_(2))/(2)`
    D
    `sqrt(K_(1) K_(2))`

  • Two rods A and B are of equal lengths. Their ends of kept between the same temperature and their area of cross-section are A_(1) and A_(2) and thermal conductivities K_(1) and K_(2) . The rate of heat transmission in the two rods will be equal, if

    A
    `K_(1) A_(2) = K_(2) A_(1)`
    B
    `K_(1) A_(1) = K_(2) A_(2)`
    C
    `K_(1) = K_(2)`
    D
    `K_(1) A_(1) = K_(2) A_(2)`

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