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Three metal rods of coefficient of therm...

Three metal rods of coefficient of thermal conductivities `K,2K,3K` conducts heats of `3Q, 2Q,Q` per seconds through unit area then the ratio of temperature gradients .

A

`9:3:1`

B

`9:1:1`

C

`3:1:1`

D

`1:1:1`

Text Solution

Verified by Experts

The correct Answer is:
A
`Q=(KA(Deltatheta)t)/(l)`
`((Deltatheta)/(l))prop(Q)/(K)"let"(Deltatheta)/(l)=XrArrXprop(Q)/(K)`
`X_(1) :X_(2):X_(3)=(Q_(1))/(K_(1)):(Q_(2))/(K_(2)):(Q_(3))/(K_(3))` .
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Knowledge Check

  • Two ends of area A of a uniform rod of thermal conductivity k are maintained at different but constant temperatures. At any point on the rod, the temperature gradient is (dT)/(dl) . If I be the thermal current in the rod, then:

    A
    `I prop A`
    B
    `I prop (dT)/(dl)`
    C
    `I prop A^(@)`
    D
    `I prop(1)/(((dT)/(dl))`

  • Two identical rods with different thermal conductivities k_(1)" & "k_(2) and different temperatures are first placed along length and then along area, then the ratio of rates of heat flow in both cases is

    A
    `(k_(1)+k_(2))/(k_(1)+k_(2))`
    B
    `(4k_(1)k_(2))/((k_(1)+k_(2))^(2))`
    C
    `((k_(1)+k_(2))^(2))/(4k_(1))`
    D
    `(4k_(1)k_(2))/((k_(1)+k_(2))^(2))`

  • Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shows below What will be the temperature T for the junction?

    A
    `200/3""^(@)C`
    B
    `100/(3)""^(@)C`
    C
    `75^(@)C`
    D
    `8/1""^(@)C`
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