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Question

Two identical conducting rods are first, connected independently to two vessels, one containing water at 100^{o}C and the other containing ice at 0^{o}C. In the second case, rods are joined end to end and are connected to t same vessels .If q_{1} and q_{2} (in g/s) are the rates of melting of ice in two cases, then the ratio of ${\mathrm{q}}_{1}/{\mathrm{q}}_{2}$ is _______.

Moderate

Solution

$\begin{array}{l}\frac{\text{Temperature difference}}{\text{Thermal resistance}}=\mathrm{L}\left(\frac{\mathrm{dm}}{\mathrm{dt}}\right)\\ \frac{\mathrm{dm}}{\mathrm{dt}}\propto \frac{1}{\text{Thermal resitance}};\mathrm{q}\propto \frac{1}{\mathrm{R}}\end{array}$

The rods are in parallel in first case and they are in series in second case.

$\frac{{\mathrm{q}}_{1}}{{\mathrm{q}}_{2}}=\frac{2\mathrm{R}}{(\mathrm{R}/2)}=4$

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In an Air conditioner compartment of a train if a material of thermal conductivity K and thickness 10 cm is required to fulfill the purpose. To do so there is a need of two glass each of thickness 1 cm with air gap of 8 cm between them. If thermal conductivity of glass and air are 1 W/mK and 0.01 W/mK then the value of K is:

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