What is temperature coefficient?

The change in velocity of sound per degree change in temperature is called as temperature coefficient.

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Why do the substances expand on heating? Explain using atomic theory.

In matter, interatomic/molecular forces bind the atoms or molecules. The potential energy due to binding force depends on the interatomic separation between the atoms and varies as shown in figure.

Let us consider two atoms A

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The density of a solid whose temperature coefficient of cubical expansion is γ is ρ_{0} at 0°C. What will be its density if it is heated to 6°C?

Let, the mass of the solid be m.

If V

...(1)

If we increase the temperature then the volume will increase.

Density will decrease because mass remains constant.

Let V be the volume and ρ be the density of the same mass of solid at temperature θ°C.

...(2)

From (1) and (2), we have

If γ is the temperature coefficient of volume expansion of solid then,

Thus,

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Two metal strips A and B, each of length L_{0} and thickness d at temperature T_{0 }be fastened together so that their ends coincide. The temperature coefficient of linear expansion of A is α_{A} and that of B is α_{B }(α_{A}> α_{B}). Find the radius of curvature of strip when it is heated.

Let us consider two strips A and B each of length L

If the strip is heated through 9°C, the length of A and B respectively is,

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A rod is clamped between two rigid supports so that it neither bends nor expands. Find the thermal compression force and thermal stress set up in the rod when it is heated through 9°C.

Consider a rod of length L, area of cross-section A, clamped between the two rigid supports so that it neither expands nor bends.

Heat the rod so that its temperature increases by θ°C.

As the rod is neither allowed to expand nor bend, therefore a compressive force or stress is set up in the rod. This force or stress is called thermal force or thermal stress.

Let be the coefficient of linear expansion and Y be the Young’s modulus of material.

If the ends of rod were free, then its length would increase by,

The rod being clamped, does not expand but a strain is produced in the rod.

The strain in the rod is given by,

The stress in the wire is,

Thermal stress = Y x strain

=

Thermal force developed in the rod is,

Thermal force = Thermal Stress x Area

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Derive the relation between a and γ. Assume that coefficient of linear expansions are same in all directions.

Let a rectangular cuboid be of sides L

Therefore the volume of cuboid at 0°C is V

When cuboid is heated, all of its sides will expand and hence volume.

If is the coefficient of linear expansion and γ is coefficient of cubical expansion, then at temperature θ°C,

and

But,

Therefore,

Since a<<1, therefore using binomial expansion,

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