The intensity of heat radiation by a point source measured by a thermopile placed at a distance $d$ is $I,$ If the distance of thermopile is doubled then the intensity of radiation will be-

A thermally isolated vessel contains $100 \mathrm{g}$ of water at $0 °\mathrm{C}$. When the air above the water is pumped out, some water freezes and some evaporates at $0 °\mathrm{C}$ itself. Then the mass of the ice formed if no water is left in the vessel. Latent heat of vaporization of water at $0 °\mathrm{C}=2.10\times {10}^6 \mathrm{J} {\mathrm{kg}}^{-1}$ and latent heat of fusion of ice$=3.36\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$.

$2 \mathrm{kg}$ ice at $-20°\mathrm{C}$ is mixed with $5 \mathrm{kg}$ water at $20°\mathrm{C}$. Then final amount of water in the mixture would be;

(Given specific heat of ice $=0.5\mathrm{cal}/\mathrm{g}°\mathrm{C}$, specific heat of water $=1\mathrm{cal}/\mathrm{g}°\mathrm{C}$ and latent heat of fusion of ice $=80\mathrm{cal}/\mathrm{g}$)

In an insulated vessel, $0.05 \mathrm{kg}$ of steam at $373 \mathrm{K}$ and $0.45 \mathrm{kg}$ of ice at $253 \mathrm{K}$ are mixed. Find the final temperature of the mixture.

Given, $L_{\mathrm{fusion}}=80 \mathrm{cal} {\mathrm{g}}^{-1}=336 \mathrm{J} {\mathrm{g}}^{-1}, L_{\mathrm{vapourization}}=540 \mathrm{cal} {\mathrm{g}}^{-1}=2268 \mathrm{J} {\mathrm{g}}^{-1}$,

$S_{\mathrm{ice}}=2100 \mathrm{J} {\mathrm{kg}}^{-1}, K=0.5\mathrm{cal} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$ and $S_{\mathrm{water}}=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}=1\mathrm{cal} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$

Assertion: Gas thermometers are more sensitive than liquid thermometers.

Reason: Coefficient of thermal expansion of gases is more than liquid.

Assertion: Water is considered unsuitable for use in thermometers.

Reason: This is due to small specific heat and high thermal conductivity.