(B) The change in temperature is $\Delta T = 40\,^{\circ}C - 27\,^{\circ}C = 13\,^{\circ}C$.The thermal expansion of a rail is given by $\Delta l = l

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(B) The change in temperature is $\Delta T = 40\,^{\circ}C - 27\,^{\circ}C = 13\,^{\circ}C$.The thermal expansion of a rail is given by $\Delta l = l \alpha \Delta T$.For the gap of width $x$ to close up, the expansion of the rail must equal the gap width, so $\Delta l = x$.Substituting the values, we get $x = l \alpha (13)$.Solving for $l$, we find $l = \frac{x}{13\alpha}$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Thermal Expansion for Solid

Medium

The gap between any two rails, each of length $l$ laid on a railway track, is equal to $x$ at $27\,^{\circ}C$. When the temperature rises to $40\,^{\circ}C$, the gap closes up. If the coefficient of linear expansion of the material of the rail is $\alpha$, the length $l$ of a rail at $27\,^{\circ}C$ is:

A
$\frac{x}{26\alpha}$
B
$\frac{x}{13\alpha}$
C
$\frac{2x}{13\alpha}$
D
$\frac{2x}{14\alpha}$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Thermal Expansion for Solid

$A$ thin copper wire of length $l$ metre increases in length by $2\%$ when heated through $10^{\circ}C$. The percentage increase in area when a square copper sheet of side $l$ metre is heated through $10^{\circ}C$ is:

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If the volume of a block of metal changes by $0.12\%$ when it is heated through $20^{\circ}C$,the coefficient of linear expansion (in per $^{\circ}C^{-1}$) of the metal is :-

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$A$ uniform metal rod of length $L$ and mass $M$ is rotating about an axis passing through one of the ends and perpendicular to the rod with angular speed $\omega$. If the temperature increases by $t^{\circ} C$, then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod $= \alpha$)

MediumTS EAMCET 2001

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$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

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$A$ cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 \times 10^{-5} /^{\circ}C$,$\alpha_y = 2 \times 10^{-5} /^{\circ}C$,$\alpha_z = 3 \times 10^{-5} /^{\circ}C$. The coefficient of superficial expansion of the faces can be:

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$A$ thin copper wire of length $l$ metre increases in length by $2\%$ when heated through $10^{\circ}C$. The percentage increase in area when a square copper sheet of side $l$ metre is heated through $10^{\circ}C$ is:

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20^{\circ}C$,the coefficient of linear expansion (in per $^{\circ}C^{-1}$) of the metal is :-

$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

$A$ cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 \times 10^{-5} /^{\circ}C$,$\alpha_y = 2 \times 10^{-5} /^{\circ}C$,$\alpha_z = 3 \times 10^{-5} /^{\circ}C$. The coefficient of superficial expansion of the faces can be:

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