Two materials having coefficients of thermal conductivity $3K and K$ and thickness d and $3\text{d}$ respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are ${\theta}_{2} and {\theta}_{1}$ respectively, \left({\theta}_{2} > {\theta}_{1}\right) . The temperature at the interface is

Question

Two materials having coefficients of thermal conductivity

3K and K

and thickness d and

3\text{d}

respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are

{\theta}_{2} and {\theta}_{1}

respectively, \left({\theta}_{2} > {\theta}_{1}\right) . The temperature at the interface is

Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively, are joined to

Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively, are joined to

Quantrex Academy · Accepted Answer

Correct answer: D. θ _ 1 10 + 9 θ _ 2 10

Let the temperature of the junction T ° C . Rate of heat flow in Rod 1 = rate of heat flow in Rod 2 (3kA)/(d)( θ _ 2 - T) = (kA)/(3d)(T - θ _ 1 ) ⇒ 9( θ _ 2 - T) = (T - θ _ 1 ) ⇒ 10T = 9 θ _ 2 + θ _ 1 ⇒ T = 9 θ _ 2 + θ _ 1 10 = θ _ 1 10 + 9 θ _ 2 10

Two materials having coefficients of thermal conductivity 3K and K...

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