Thermal Expansion

A thin aluminium plate has an area $286 {\mathrm{cm}}^2$ at $20 °\mathrm{C}$ Find its area when it is heated to $180 °\mathrm{C}$ ($\beta$ for aluminium =$4.9\times {10}^{-5 }°{\mathrm{C}}^{-1})$)

A brass rod and a lead rod each $80 \mathrm{cm}$ long at $0°\mathrm{C}$ are clamped together at one end with their free ends coinciding. The separation of free ends of the rods if the system is placed in a steam bath is (${\alpha }_{brass}=18\times {10}^{-6} °{\mathrm{C}}^{-1}, {\alpha }_{\mathit{l}\mathit{e}\mathit{a}\mathit{d}}=28\times {10}^{-6} °{\mathrm{C}}^{-1}$ )

Give an example of volume expansion of a liquid on heating. The area of a solid substance at a temperature of $T_{1 }\mathrm{K}$ is $A_1 {\mathrm{m}}^2$ and that at a temperature of $T_2 \mathrm{K}$ is$A_2 {\mathrm{m}}^2$ . Write down the mathematical expression for the coefficient of area expansion with unit, of that solid substance

 If the temperature of body is increased by $200°\mathrm{C}$ then the percentage decrease in its density is [$\gamma = (3.75 \times {10}^{-5}{)}^{\circ }\mathrm{C}$]
 

A pendulum clock keeps correct time at $0°\mathrm{C}$. Mean coefficient of linear expansion is $\alpha °{\mathrm{C}}^{-1}$. If the temperature of the room rises by a small amount of $t°\mathrm{C}$, then find the ratio of time period at $t°\mathrm{C}$ to $0°\mathrm{C}$

A thin metal wire of length $l$ increases in length by $0.1\%$ on heating it from temperature ${\theta }_1$, to ${\theta }_2$. If a plate of the same material is heated from ${\theta }_1$ to ${\theta }_2$, which has dimensions $2l\times 3l$, then percentage increase in its area is

The internal volume of a glass flask is $V {\mathrm{cm}}^3$, how much volume of mercury is kept in the flask so that the volume of the empty part of the flask remains the same at all elevations? (Volume expansion coefficient of mercury is $1.8\times {10}^{-4} °\mathrm{C}$ and linear expansion coefficient of glass $=9\times {10}^{-6} °\mathrm{C}$).

A long cylindrical vessel of volume $V$ and coefficient of linear expansion $\alpha$ contains a liquid. The level of liquid has not changed on heating. The coefficient of real expansion of the liquid is

${\gamma }_A$ of liquid is $\frac{7}{8}$ of ${\gamma }_R$ of liquid. ${\alpha }_g$ of vessel is

A hole of diameter $5 \mathrm{cm}$ is drilled in a metal sheet at $30 °\mathrm{C}$. The linear expansion of metal is $2\times {10}^{-5} {\mathrm{K}}^{-1}$. The diameter of the hole when the temperature is raised to $230 °\mathrm{C}$, is equal to

Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \mathrm{cm}$ longer than the copper rod at any temperature.
[The coefficient of linear expansion for steel and copper are $1.1\times {10}^{-5} {}^{\circ }\mathrm{C}$ and $1.7\times {10}^{-5} {}^{\circ }\mathrm{C}$ respectively]

Take two bottles of the same size. Tie a ballon to the mouth of each bottle, and place one bottle in a tub of hot water while the other bottle in the tub having ice. What will you observe after some time?

A metal tape is calibrated at $25°\mathrm{C}$. On a cold day when the temperature is $-15°\mathrm{C}$, the percentage error in the measurement of length is
(Coefficient of linear expansion of metal $=1\times {10}^{-5}{}^{\circ }\mathrm{C}^{-1}$)

A lamp post of negligible mass of length $l$ and cross sectional area $S=10 {\mathrm{cm}}^2$ is made of material with linear expansion coefficient $\alpha =1.1\times {10}^{-5} {\mathrm{K}}^{-1}$ and Young 's modulus $Y=2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. If temperature of lamp post is raised by $\Delta T=10 \mathrm{K}$ then a mass $m\left(\times {10}^2\right)\mathrm{kg}$ should be put on the lamp post, so that there is no change in the length of lamp post, the value of $\frac{m}{11}$ is ( take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A metal bar is $2.4 \mathrm{m}$ long. After heating, it's length increases by $2\%$. What is the new length?

The coefficient of cubical expansion of a solid is $27 \times {10}^{-6}° {\mathrm{C}}^{-1}$. If the temperature is measured on Fahrenheit scale, numerical value of coefficient of linear expansion of solid is

A hollow metallic cube has edge length $12\mathrm{cm}$. A liquid whose coefficient of volume expansion is $6\times {10}^{-10}{{}^{\circ }\mathrm{C}}^{-1}$ is poured into it upto height $3\mathrm{cm}$. When temperature increases, height of liquid in cube remains unchanged. Coefficient of linear expansion of cube's material is $n\times {10}^{-10}{{}^{\circ }\mathrm{C}}^{-1}$, find $n$.

A uniform copper rod of length $50 \mathrm{cm}$ and diameter $3.0 \mathrm{mm}$ is kept on a frictionless horizontal surface at $20°\mathrm{C}$. The coefficient of linear expansion of copper is $2.0\times {10}^{-5}{ \mathrm{K}}^{-1}$ and Young's modulus is $1.2\times {10}^{11}$ $\mathrm{N} {\mathrm{m}}^{-2}$. The copper rod is heated to $100°\mathrm{C}$, then the tension developed in the copper rod is

Derive ${\alpha }_v=\frac{1}{T}$. for an Ideal gas .

An experiment is performed to measure the coefficient of linear expansion of glass.
Experiment: A glass cylinder is filled completely by $100\mathrm{gm}$ of mercury at temperature $0°\mathrm{C}.$ When the temperature of the cylinder is increased upto $\mathrm{\theta }=20°\mathrm{C},$ now it is observed that the cylinder can contain $99.7\mathrm{gm}$ of mercury. In both the cases the temperature of the mercury is assumed to be equal to that of the cylinder. It is known that coefficient of volume expansion of mercury is ${\gamma }_m=\frac{18\times {10}^{-5}}{{}^{\circ }\mathrm{C}}.$ The coefficient of linear expansion of glass measured from the experiment is $\frac{\alpha \times {10}^{-5}}{{}^{\circ }\mathrm{C}.}.$

Find the value of $\alpha$