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

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 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 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

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)

A simple seconds pendulum is constructed out of a very thin string of thermal coefficient of linear expansion $\alpha =20\times {10}^{-4} °{\mathrm{C}}^{-1}$ and a heavy particle attached to one end. The free end of the string is suspended from the ceiling of an elevator at rest. The pendulum keeps the correct time at $0 °\mathrm{C}$. When the temperature rises to $50 °\mathrm{C}$, the elevator operator of mass $60 \mathrm{kg}$ being a student of physics accelerates the elevator vertically, to have the pendulum's correct time. Find the apparent weight (kg wt) of the operator when the pendulum keeps the correct time at $50 °\mathrm{C}$. $\left(\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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

A uniform steel wire of cross sectional area $0.20{ \mathrm{mm}}^2$ is held between two clamps. Find the extra force exerted by each lamp on wire if it is cooled from $100°\mathrm{C}$ to $0°\mathrm{C}$.

Given: Young's modulus of the steel $Y=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$, coefficient of linear expansion of steel $\alpha =1.2\times {10}^{-5} °{\mathrm{C}}^{-1}$.

Given when a tensile force of $33000 \mathrm{N}$ is applied on a steel rod, there is some change in length. Find the change of temperature required to produce the same elongation, if the steel rod is heated.

(The modulus of elasticity is $3\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$, area of cross-section$={10}^{-3} {\mathrm{m}}^2$ and the coefficient of linear expansion of steel is $1.1\times {10}^{-5} {}^{\circ }\mathrm{C}^{-1}$). $$   $$