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Two bars of thermal conductivities K and...

Two bars of thermal conductivities `K` and `3K` and lengths `1 cm` and `2 cm` respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is `0^(@)C` and `K^(2)//l` respectively (see figure), then the temperature `phi` of the interface is

A

`50^(@)C`

B

`100/3.^(@)C`

C

`60^(@)C`

D

`200/3.^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
C
Temperature of interface
`theta = (K_(1)theta_(1)l_(2)+K_(2)theta_(2)l_(1))/(K_(1)l_(2)+K_(2)l_(1)) = (Kxx0xx2+3Kxx100xx1)/(Kxx2+3Kxx1)`
`=(300K)/(5K) = 60^(@)C`.
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Knowledge Check

  • Two rods having thermal conductivity in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is 100^(@)C and free end of the second rod is 20^(@)C . Then temperature of the junction is

    A
    `70^(@)C`
    B
    `50^(@)C`
    C
    `50^(@)C`
    D
    `90^(@)C`

  • Three rods A, B and C of the same length and same cross-sectional area are joined as shown. Their thermal conductivities are in the ratio 1:2:3/2. If the open ends of A and C are at 200^@ C and 18^@ C, respectively, then the temperature at the junction of A at steady state is

    A
    `156^@C`
    B
    `148^@C`
    C
    `116^@C`
    D
    `74^@C`

  • Two rods of similar area of cross section and length are joined as shown in the figure. The ratio of their thermal conductivity is 2:3. The free ends are maintained at 100^(@)C and 0^(@)C respectivley. THE temperature at junction in steady state is

    A
    `50^(@)C`
    B
    `40^(@)C`
    C
    `60^(@)`
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    `80^(@)C`
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