The rod connecting two reservoirs and connected to a source is as shown in diagram. The rod is in steady state. Find the temperature of source, so that rate of melting of ice is 16 times that rate of vaporization. (Latent heat of vaporization is 540 Cal/gm and latent heat of fusion is 80 Cal/gm)

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The source is at T; the left path to steam is twice the right path to ice.
$\overset{m}{˙}_{ice} = 16 \overset{m}{˙}_{steam}$
$\dot{Q}_{steam} = \frac{T - 100}{2 ℓ / ( 3 A k )} = \overset{m}{˙}_{steam} L_{v}$
$\dot{Q}_{ice} = \frac{T}{ℓ / ( 3 A k )} = 16 \overset{m}{˙}_{steam} L_{f}$
$\frac{T - 100}{2 T} = \frac{L _{v}}{16 L _{f}} = \frac{540}{16 \times 80}$
$\frac{T - 100}{T} = \frac{27}{32}$
$T = 64 0^{\circ} C$
Answer C.

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