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

The temperature of an isotropic cubical solid of length $l_0$, density ${\rho }_0$ and coefficient of linear expansion $\alpha$ is increased by $20°\mathrm{C}$. Then at higher temperature, to a good approximation:-

A glass rod when measured with a zinc scale, both being at $30°\mathrm{C}$, appears to be of length $100 \mathrm{cm}$. If the scale shows correct reading at $0°\mathrm{C}$, then the true length of glass rod at $30°\mathrm{C}$ and $0°\mathrm{C}$ are:-
$\left({\alpha }_{\mathrm{glass} }=8\times {10}^{-6}{{}^{\circ }\mathrm{C}}^{-1},{\alpha }_{\mathrm{zinc} }=26\times {10}^{-6}{ \mathrm{K}}^{-1}\right)$

Two fine steel wires, fastened between the projections of a heavy brass bar, are just taut when the whole system is at $0°\mathrm{C}$. What is the tensile stress in the steel wires when the temperature of the system is raised by $200°\mathrm{C}$ ? $\left({\alpha }_{\mathrm{brass} }=2\times {10}^{-5}{{}^{\circ }\mathrm{C}}^{-1},{\alpha }_{\mathrm{steel} }=1.2\times {10}^{-5}{{}^{\circ }\mathrm{C}}^{-1},Y_{\mathrm{steel} }=200 G\mathrm{N} {\mathrm{m}}^{-2}\right)$

In a mercury-glass thermometer the cross-section of the capillary portion is $A_0$ and the volume of the bulb is $V_0$ at $273 \mathrm{K}$. If $\alpha$ and $\gamma$ are the coefficients of linear and cubical expansion coefficients of glass and mercury respectively then length of mercury in the capillary at temperature $t°\mathrm{C}$ is (Ignore the increase in cross-sectional area of capillary)

$5 \mathrm{g}$ of steam at $100°\mathrm{C}$ is mixed with $10 \mathrm{g}$ of ice at $0°\mathrm{C}$. Choose correct alternative/s):-(Given $s_{water }=1\mathrm{cal} {\left(\mathrm{g}°\mathrm{C}\right)}^{-1}$, $L_F=80 \mathrm{cal} {\left(\mathrm{g}\right)}^{-1}, L_V=540 \mathrm{cal} {\mathrm{g}}^{-1}$).

$n$ moles of an ideal triatomic linear gas undergoes a process in which the temperature changes with volume as $T=k_1{ V}^2$ where $k_1$ is a constant. Choose incorrect alternative:-

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. What is. the molar specific heat at constant pressure of mixture ?

A inert gas obeys the law $P{V}^x=$ constant. For what value of $x$, it has negative molar specific heat-