Physics · Thermal Properties Of Matter · NEET
It is the fractional change in volume per unit rise in temperature. In symbols, gamma = (delta V / V) / delta T, so delta V = gamma V delta T. Example: if gamma = 5 x 10^-5 per degree C and you heat 1 litre of oil by 20 degrees C, the extra volume is delta V = (5 x 10^-5)(1000 cm^3)(20) = 1 cm^3.
Per kelvin (K^-1), which is the same size of unit as per degree Celsius (per degree C), because a change of 1 K equals a change of 1 degree C. Gamma is a small number for solids and liquids, so it is written with powers of ten, like 2 x 10^-5 K^-1.
For an isotropic solid (same expansion in every direction) yes, gamma = 3 alpha, and also beta = 2 alpha. But liquids and gases have no alpha, so gamma is measured directly for them. For anisotropic crystals the three directions differ, and gamma equals the sum of the three separate linear coefficients.
No. delta V = gamma V delta T uses only the volume V, not the shape. A cube, sphere, or irregular blob of the same material and same starting volume all gain the same delta V for the same delta T. Only V, gamma, and delta T matter.
In a liquid the particles are loosely bound and free to move, so heating pushes them apart more easily than in a tightly bonded solid. That is why gamma for liquids is typically 10 times or more larger than gamma for solids, which is why a liquid overflows a container that was heated together with it.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
delta V = gamma V delta T, where delta V is the increase in volume, gamma is the coefficient of cubical expansion, V is the original volume, and delta T is the rise in temperature. The final volume is V' = V (1 + gamma delta T).
For most solids gamma is around 1 x 10^-5 to 7 x 10^-5 K^-1. For liquids it is larger, for example mercury is about 18 x 10^-5 K^-1 and water is about 21 x 10^-5 K^-1 near room temperature. Gases have a much larger gamma, about 3.7 x 10^-3 K^-1.
Since mass stays the same but volume grows, density falls on heating. Approximately, new density = old density / (1 + gamma delta T), which for small delta T is about old density x (1 - gamma delta T). This is why hot fluids are lighter and rise.
For solids and most liquids gamma is nearly constant over an ordinary temperature range, so we treat it as fixed for NEET numericals. It can vary at very high temperatures and near phase changes, and water is a special case (anomalous expansion below 4 degrees C).
