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:-

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)