Physics · Thermal Properties Of Matter · NEET
Yes. From delta L = L alpha delta T, a longer rod expands more for the same temperature rise. A 2 metre rod stretches twice as much as a 1 metre rod of the same material. But alpha itself does not depend on length; alpha is a material property. Only the actual increase delta L scales with L.
From alpha = delta L / (L delta T), delta L and L are both lengths (metre), so they cancel. What is left is 1 / temperature. So the SI unit is per kelvin, written K^-1 (same as per degree Celsius, since a 1 K change equals a 1 degree C change). Alpha has no length unit.
The hole gets BIGGER. Every part of the metal expands outward together, as if the hole were filled with the same metal. So a hole, a gap, or a cavity expands just like solid metal. This is why a blacksmith heats an iron ring to slip it onto a wheel: the inner hole grows.
delta L is the actual increase in length in metres, and it changes with the rod length and the temperature rise. Alpha is a fixed number for a given material (like 1.7 x 10^-5 K^-1 for copper) that measures how strongly that material expands. Alpha is the cause; delta L is the result you measure.
In a solid the atoms are held tightly by strong bonds and only vibrate a little more when heated. So the spacing between atoms grows by only a tiny fraction per degree. That is why a 1 metre steel rod grows only about 0.011 mm per degree. Gases have no such bonds, so gases expand far more than solids.
A copper rod of length 88 cm and an aluminium rod of unknown length have their increase in length independent of the increase in temperature. The length of the aluminium rod is: (alpha_Cu = 1.7 x 10^-5 K^-1, alpha_Al = 2.2 x 10^-5 K^-1)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
delta L = L alpha delta T, where delta L is the increase in length, L is the original length, alpha is the coefficient of linear expansion, and delta T is the temperature rise. The new length is L' = L (1 + alpha delta T).
Alpha is the fractional increase in length of a material per 1 degree rise in temperature. If alpha = 1.7 x 10^-5 K^-1 for copper, then each metre of copper grows by 1.7 x 10^-5 metre for every 1 degree of heating.
Per kelvin, written K^-1. It is the same numerically as per degree Celsius because a change of 1 kelvin equals a change of 1 degree Celsius.
For small temperature changes we treat alpha as a constant. Over very large temperature ranges alpha varies slightly, but for NEET problems you use a fixed value.
For an isotropic solid, the area expansion coefficient beta = 2 alpha and the volume expansion coefficient gamma = 3 alpha. So alpha : beta : gamma = 1 : 2 : 3.
