A Carnot heat engine has an efficiency of $10 \%$. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is

The rms velocity of a gas molecules oí mass $m$ at a given temperature is proportional to

Match the following．

(a) Thermal conductivity	(i) $\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]$
(b) Boltzmann constant	(ii) $\left[M^0 L^2 T^{-2} K^{-1}\right]$
(c) Latent heat	(iii) $\left[M L^2 T^{-2} K^{-1}\right]$
(d) Specific heat	(iv) $\left[M^0 L^2 T^{-2}\right]$

The length of a metal bar is 20 cm and the ares of cross-section is $4 \times 10^{-4} \mathrm{~m}^2$. If one end of the rod is kept in ice at $0^{\circ} \mathrm{C}$ and the other end is kept in steamat $100^{\circ} \mathrm{C}$, the mass of ice melted in one minute is 5 g , the thermal conductivity of the matal in $\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ is (Latent heat of fusion $=80 \mathrm{cal} / \mathrm{g}$ )