Embibe Experts Solutions for Chapter: Thermal Properties of Matter, Exercise 2: Exercise-2

Two rods identical in geometry but of different materials having co-efficient of thermal expansion ${\alpha }_1 \& {\alpha }_2$ and Young’s modulii $Y_1 \mathrm{\&} Y_{2 }$respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If ${\alpha }_1 : {\alpha }_2 = 2 : 6$ the thermal stresses developed in the two rods are equal provided $Y_1 : Y_2$ is equal to :

$2 \mathrm{kg}$ 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 $S_{\mathrm{water}}=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}=1\mathrm{cal} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$

What is the ratio$\frac{k_1}{k_2}$ Can be expressed. When a block of iron floats in mercury at $0°\mathrm{C}$, fraction $k_1$ Of its volume is submerged, while at the temperature $60°\mathrm{C}$, a fraction $k_2$ is seen to be submerged. If the coefficient of volume expansion of iron is ${\gamma }_{Fe}$ And that of mercury is ${\gamma }_{Hg}$,

A hot wire of copper is stretched at a temperature of $150°\mathrm{C}$ between two fixed walls. At what temperature will the wire break when it is cooled? The breaking stress of copper is $2.45\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}$ Young's modulus of copper $=11.8\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2},$ coefficient of linear expansion of copper $=1.6\times {10}^{-5} °{\mathrm{C}}^{-1}.$

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.

Assertion: Latent heat is the heat required to melt a unit mass of solid.

Reason: Melting of solid causes no change in internal energy.