Thermal Expansion

The absolute coefficient of expansion of a liquid is $7$ times that the volume coefficient of expansion of the vessel. The ratio of absolute and apparent expansion of the liquid is

 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 $=9\times {10}^{-6} °\mathrm{C}$).

The coefficient of apparent expansions of a liquid in two different vessels are $a$ and $b$. Then the real coefficient of expansions of liquid, if the ratio of volume expansion of vessels is $x:y$, is

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]

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 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

What is thermal stress?

An aluminium cube of side $20 \mathrm{cm}$ floats on mercury. The temperature of the system increases from $300 \mathrm{K}$ to $350 \mathrm{K}$. Given that the density of aluminium and mercury at $300 \mathrm{K}$ are $2.7 \mathrm{g} \mathrm{c}.{\mathrm{c}}^{-1}$ and $13.6 \mathrm{g} \mathrm{c}.{\mathrm{c}}^{-1}$. while the coefficient of volume expansion of mercury and linear expansion of aluminium are $1.8\times {10}^{-4}/°\mathrm{C}$ and $23\times {10}^{-6}/°\mathrm{C}$ respectively

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 $\alpha$

A block is hung by means of two identical wires having cross section area $A\left(1{ \mathrm{mm}}^2\right)$ as shown in the diagram. If temperature is lowered by $\Delta T\left(10°\mathrm{C}\right),$ find the mass (in $\mathrm{kg}$ ) to be added to hanging mass such that junction remains at initial position. Given that co-efficient of linear expansion $\alpha =\frac{2\times {10}^{-5}}{{}^{\circ }\mathrm{C}}$ and Young's modulus $Y=5\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ for the wire.

A wire is made by attaching two segments together end to end. One segment is made of aluminium and the other is steel. The effective coefficient of linear expansion of the two segment wire is $19\times {10}^{-6} °{\mathrm{C}}^{-1}$. The fraction length of aluminium is $\frac{x}{11}$ then find $x$. (linear coefficients of thermal expansion of aluminium and steel are $23\times {10}^{-6} °{\mathrm{C}}^{-1}$ and $12\times {10}^{-6} °{\mathrm{C}}^{-1}$ respectively)