A composite rod is made by joining two sections in series. The first section has a thermal conductivity 3K_0 , length L , and cross-sectional area A . The second section has a thermal conductivity K_0 , length L , and

Question

Quantrex Academy · Accepted Answer

Correct answer: B. (75 K_0 A)/(L L_f)

Let the temperature of the junction in steady state be

T

.

The rate of heat flow through both sections must be equal:

H = \dfrac{3K_0 A (100^{\circ}\mathrm{C} - T)}{L} = \dfrac{K_0 A (T - 0^{\circ}\mathrm{C})}{L}

\Rightarrow 300 - 3T = T

\Rightarrow 4T = 300 \Rightarrow T = 75^{\circ}\mathrm{C}

The steady heat current is:

H = \dfrac{K_0 A (75 - 0)}{L} = \dfrac{75 K_0 A}{L}

Alternatively, the equivalent thermal resistance is

R_{eq} = \dfrac{L}{3K_0 A} + \dfrac{L}{K_0 A} = \dfrac{4L}{3K_0 A}

.

The heat current is

H = \dfrac{\Delta T}{R_{eq}} = \dfrac{100}{\dfrac{4L}{3K_0 A}} = \dfrac{75 K_0 A}{L}

.

The heat reaching the ice is used to melt it. If

\dfrac{dm}{dt}

is the mass of ice melted per unit time, then:

H = \dfrac{dm}{dt} L_f

\Rightarrow \dfrac{dm}{dt} = \dfrac{75 K_0 A}{L L_f}

Answer:

\dfrac{75 K_0 A}{L L_f}

A composite rod is made by joining two sections in series. The...

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