Physics · Thermal Properties Of Matter · NEET
A solid expands equally in all three directions (length, width, depth). Each linear dimension grows by the fraction alpha delta T. Volume depends on all three, so the fractional volume change is about 3 times the fractional length change: delta V / V = 3 alpha delta T. NCERT derives this from a cube: delta V is about 3 l^2 delta l, which gives gamma = 3 alpha. The number 3 comes from the 3 dimensions, not from the sphere shape.
No. For any solid made of the same material, delta V = 3 alpha V delta T. The 3 alpha part depends only on the material, not the shape. A cube, a rod, and a sphere of the same material and same volume all show the same fractional volume increase. The sphere only matters when you replace V with (4/3) pi R^3 to get a form in terms of radius R.
Start with delta V = 3 alpha V delta T and put V = (4/3) pi R^3. Then delta V = 3 alpha delta T x (4/3) pi R^3. The 3 and the 1/3 cancel, leaving delta V = 4 pi R^3 alpha delta T. Students who forget to cancel keep a stray 4/3 and pick a wrong option.
Yes. A uniform solid sphere expands by the same fraction in every direction, so it grows into a larger sphere of radius R + delta R with delta R = alpha R delta T. It does not become an ellipse or bulge, because alpha is the same in all directions for an isotropic material.
Both follow the same rule. A solid sphere and a spherical cavity (hole) of the same size in the same material expand by delta V = 3 alpha V delta T. A hole expands as if it were filled with the surrounding material, so cavities get bigger on heating, not smaller.
The temperature of a metallic sphere of radius R is increased by a small amount delta T. If the linear coefficient of thermal expansion of the metal is alpha, the approximate increase in the volume of the sphere is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
delta V = 3 alpha V delta T, where alpha is the linear expansion coefficient and V is the original volume. Putting V = (4/3) pi R^3 gives delta V = 4 pi R^3 alpha delta T.
A solid expands in 3 directions at once, each by the fraction alpha delta T, so the fractional volume change is 3 times the fractional length change. Hence gamma = 3 alpha.
The radius grows by delta R = alpha R delta T, since each linear dimension follows the linear expansion rule delta L = alpha L delta T.
Yes. The material and any cavity both expand by delta V = 3 alpha V delta T. A cavity expands as if it were solid material, so the hole gets larger on heating.
Both have units of per kelvin (K^-1) or per degree Celsius, because they measure a fractional change per unit temperature rise.
