Question

Three rods of material x and two rods of material y are connected as shown in the figure here. All the rods are identical (each 1 cm long and of cross-sectional area $100c{m}^2$). At the junctions A and C, there are two sources of heat 25W and 100 W, and at B and at D there are two sinks maintained at ${30}^{\circ }C$ and ${10}^{\circ }C$, respectively. Calculate the temperatures of the points A and C in the steady state. The thermal conductivity of x is $200J{s}^{-1}{m}^{-1}{K}^{-1}$ and that of y is $400J{s}^{-1}{m}^{-1}{K}^{-1}$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The direction of heat flow is shown in the figure.

By the point rule
$100=\frac{400\times {10}^{-2}({\theta }_C-30)}{1}+\frac{400\times {10}^{-2}({\theta }_C-10)}{1}+\frac{200\times {10}^{-2}({\theta }_C-{\theta }_A)}{1}or,260=10{\theta }_C-2{\theta }_A\frac{200\times {10}^{-2}({\theta }_C-{\theta }_A)}{1}+25=\frac{200\times {10}^{-2}({\theta }_A-30)}{1}+\frac{200\times {10}^{-2}({\theta }_A-10)}{1}\Rightarrow 105=6{\theta }_A-2{\theta }_{C}Hence,{\theta }_A={28.0}^{\circ }Cand{\theta }_C={31.6}^{\circ }C$