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Explain thermal expansion of solids on the basis of the potential energy curve.
The potential energy curve is the variation of the potential energy between atoms or molecules in a solid with respect to their separation distance and can be used to explain thermal expansion of solids. At absolute zero temperature, atoms in a solid are at their equilibrium positions where the poteRead more
The potential energy curve is the variation of the potential energy between atoms or molecules in a solid with respect to their separation distance and can be used to explain thermal expansion of solids.
At absolute zero temperature, atoms in a solid are at their equilibrium positions where the potential energy is at its minimum. With increasing temperature, atoms vibrate more violently and average separation between them increases because kinetic energy of atoms increases with temperature.
The curve of potential energy shows that the atoms are moving apart, and this is when the potential energy increases. The system comes to a new equilibrium position in which the atoms are at a slightly larger separation, thus causing the expansion of the solid. The amplitude of atomic vibrations increases with temperature, which leads to an overall expansion of the material.
In solids, the thermal expansion is uniform in all directions, linear, superficial, or cubical depending on the nature of the solid and its temperature change.
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Define coefficient of superficial expansion and give its units.
It is the fractional change in the surface area of a substance for a unit change in temperature, when heated or cooled at constant pressure. It is defined mathematically as: α = (1/A) * (dA/dT) where, - α is the coefficient of superficial expansion - A is the initial surface area - dA is the changeRead more
It is the fractional change in the surface area of a substance for a unit change in temperature, when heated or cooled at constant pressure. It is defined mathematically as:
α = (1/A) * (dA/dT)
where,
– α is the coefficient of superficial expansion
– A is the initial surface area
– dA is the change in surface area
– dT is the change in temperature.
The units of α are per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹).
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Define coefficient of cubical expansion. Write an expression for it. Give its units.
The coefficient of cubical expansion (β) of a substance is the fractional change in its volume for a unit change in temperature, when the substance is heated or cooled at constant pressure. Mathematically, it is defined as: β = (1/V) * (dV/dT) where: - β is the coefficient of cubical expansion, - VRead more
The coefficient of cubical expansion (β) of a substance is the fractional change in its volume for a unit change in temperature, when the substance is heated or cooled at constant pressure.
Mathematically, it is defined as:
β = (1/V) * (dV/dT)
where:
– β is the coefficient of cubical expansion,
– V is the initial volume,
– dV is the change in volume,
– dT is the change in temperature.
The units of β are per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹).
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Show that the coefficient of cubical expansion of an ideal gas at constant pressure is equal to the reciprocal of its absolute temperature.
We know that for an ideal gas at constant pressure, the volume is given by V = nRT where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature. Now, for a small change in temperature, the change in volume can be written as: dV = βV dT where βRead more
We know that for an ideal gas at constant pressure, the volume is given by
V = nRT
where V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature.
Now, for a small change in temperature, the change in volume can be written as:
dV = βV dT
where β is the coefficient of cubical expansion and dT is the change in temperature.
From the equation of state, V = nRT, we have:
dV = nR dT
Comparing the two expressions for dV, we get:
βV = nR / V
Since V = nRT, we can substitute this into the above equation:
β = 1 / T
Therefore, the coefficient of cubical expansion β for an ideal gas at constant pressure is equal to the reciprocal of its absolute temperature.
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Describe the working principle of a platinum resistance thermometer.
The platinum resistance thermometer works on the principle that the electrical resistance of platinum is a changing function of temperature. The thermometer is a platinum wire whose resistance varies linearly with temperature. The resistance is measured using a Wheatstone bridge or other precise cirRead more
The platinum resistance thermometer works on the principle that the electrical resistance of platinum is a changing function of temperature.
The thermometer is a platinum wire whose resistance varies linearly with temperature. The resistance is measured using a Wheatstone bridge or other precise circuit. By calibrating the resistance at known temperatures, the thermometer can determine an unknown temperature. Platinum is used because of its stability, wide temperature range, and predictable resistance-temperature relationship.
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