Thermal Expansion

A steel metre scale is to be ruled so that the millimetre intervals are accurate to about $5\times 10-5 \mathrm{mm}$ at a certain temperature. The maximum temperature variation allowed during ruling is (the co-efficient of linear expansion of steel $=10\times 10-6 \mathrm{K}-1)$

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

If the volume of a block metal changes by$0.12\%$, when it is heated through $20 \mathrm{℃}$, then the coefficient of linear expansion is

An iron plate is uniformly heated from $20°\mathrm{C}$ to $80°\mathrm{C}$. The change in diameter of a circular hole of diameter $1\mathrm{m}$ is $\frac{\mathrm{x}}{100}\mathrm{cm}$. Find the value of $\mathrm{x}$. $\left(\alpha =12\times {10}^{-6}/°\mathrm{C}\right)$

The water pipes burst because the water inside them is expanding when it undergoes _____.

_____is an expansion when a solid is heated and there is a change in its volume.

An ideal gas is expanding such that $p{T}^2$= constant. The coefficient of volume expansion of the gas is $\frac{n}{T}$, then find $n$.

A hole is drilled in a copper sheet. The diameter of the hole is $4.24 \mathrm{cm}$ at $27°\mathrm{C}$. What is the change in the diameter (in $\mathrm{cm}$) of the hole when the sheet is heated to $227°\mathrm{C}$ ? Coefficient of linear expansion of copper is $1.70\times {10}^{-5} °{\mathrm{C}}^{-1}$.

A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times {10}^{-5}/{}^{\text{o}}\text{C}$ along the x-axis and $5\times {10}^{-6}/{}^{\text{o}}\text{C}$ along the y and the z-axis. If the coefficient of volume expansion of the solid is $\text{C}\times {10}^{-6}/{}^{\text{o}}\text{C}$ then the value of $\mathrm{C}$ is _____________

A large steel wheel is to be fitted on a shaft of the same material. At 27^oC, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using dry ice. At what temperature (in $°\mathrm{C}$) (to the nearest integer) of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range.

[${\alpha }_{\text{steel}}=1\text{.}20\times 10^{-5}/\text{K}$]

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

Ratio of linear, area and volume expansion in solids 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 $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$)

The graph shows the change in volume of water as its temperature is raised from $0°\mathrm{C}$. What is this behaviour of water called?
   

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 square plate has three circular holes of the same radius so that centre of each hole is equidistant from the centre of the square plate. A $∆\mathrm{ABC}$ can be formed by joining the centres of the holes as shown in the figure. The plate is placed on a frictionless horizontal surface. If we increase the temperature, then

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

When temperature of water is reduced below _____$℃$, it expands.

Observe the given graph and choose the name of the process represented in the figure.

A steel rod, clamped at its two ends, rests on a fixed horizontal base. The rod is unstrained at $20 °\mathrm{C}.$ The absolute value of the longitudinal strain developed in the rod if the temperature rises to $60 °\mathrm{C}$ is.

(coefficient linear expansion of steel $=1.2\times {10}^{-5}/ °\mathrm{C}$)