Thermal Expansion

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$, $\alpha$ and $Y$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young’s modulus of its material, then for an increase in temperature of the rod by $∆T$, the longitudinal stress developed in the rod is

What is the coefficient of volume expansion of an ideal gas?

Most matter contracts on heating and expands on cooling (Yes\No).

Co-efficient of linear expansion for ionic solid is ${\mathrm{\alpha }}_{\mathrm{i}}$ and for non-ionic solid be ${\mathrm{\alpha }}_{\mathrm{n}}$ then

Length of a wire at room temperature is $4.55 \mathrm{m}$. When the temperature increases upto $100 \mathrm{℃}$, then its length becomes $4.57 \mathrm{m}$. The coefficient of linear expansion $\left(\alpha \right)$ of the given wire is

A steel wire of uniform cross-section of $1 {\mathrm{mm}}^2$ is heated upto $50°\mathrm{C}$ and clamped rigidly at its ends. If the temperature of wire falls to $40°\mathrm{C},$ change in tension in the wire is (coefficient of linear expansion of steel is $1.1\times {10}^{-5} {}^{\mathrm{o}}\mathrm{C}^{-1}$ and Young's modulus of elasticity of steel is $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$)

A metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t°\mathrm{C},$ the linear stress developed in it is

A metal rod of length $L$ and cross-sectional area $A$ is heated through $T °\mathrm{C}.$ What is the force required to prevent the expansion of the rod lengthwise?

If there is an increase in the _____ of a solid body due to heating, then the expansion is called cubical expansion.

When the temperature of water decreases from _____ $°\mathrm{C}$ to $0 °\mathrm{C}$ instead of contracting it expands, and becomes less dense.

A metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t°\mathrm{C},$ the linear stress developed in it, is

A metal rod of cross-sectional area ${10}^{-4} {\mathrm{m}}^2$ is hanging in a chamber kept at $20°\mathrm{C}$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5\times {10}^{-6} {\mathrm{K}}^{-1}$ and its Young's modulus is $4\times {10}^{12} \mathrm{N} {\mathrm{m}}^{-2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \mathrm{N}$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is

Draw a graph showing the variation of coefficient of volume expansion $\left({\alpha }_v\right)$ of copper with temperature $\left(T\right)$. What can you say about the variation of $\left({\alpha }_v\right)$ at higher temperatures using this graph? 

The coefficient of volume expansion $\left({\alpha }_v\right)$for metals like copper: 

A copper wire is held at the two ends by rigid supports. At $30°\mathrm{C}$, the wire is just taut, with negligible tension. Find the speed of transverse waves(in $\mathrm{m} {\mathrm{s}}^{-1}$ and in closest integer) in this wire at $10°\mathrm{C}$. Given: Young modulus of copper, $Y=1.3\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. Coefficient of linear expansion of copper,$\alpha =1.7\times {10}^{-5} °{\mathrm{C}}^{-1}$. Density of copper,$\rho =9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$.

Ethyl alcohol expands less than mercury for the same rise in temperature.

The amount of thermal expansion in solids does not depend on their sizes.

In which of the following devices the bending of bimetallic strip due to thermal expansion is not used?

A steel rod with a length of $0.350 \mathrm{m}$ and an aluminium rod with length of $0.250 \mathrm{m}$, both with same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is now raised by ${60}^{\mathrm{o}}\text{C}$. The length of combined rods remains the same, but the length of individual rods change. Stress developed in each rod is $\beta \times {10}^7 \mathrm{N} {\mathrm{m}}^{-2}$. Write the value of $\left[\beta \right],$where $\left[ \right]$ is the greatest integer function.
Given: ${\alpha }_s=1.2\times {10}^{–5}{ }^{\mathrm{o}}{\mathrm{C}}^{-1}, {\alpha }_{Al}=2.4\times {10}^{–5}{ }^{\mathrm{o}-}{\mathrm{C}}^{-1}, Y_s=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2} \& Y_{Al}=0.7\times {10}^{11}\mathrm{N} {\mathrm{m}}^{-2}$$$

The volume of a metal sphere increases by $0.24 \%$ when its temperature is raised by $40 °\mathrm{C}$ . The coefficient of linear expansion of the metal is