1. A liquid is held in a container. When it is heated, both the container and the liquid expand. The expansion of the container is usually very small compared to that of the liquid in it. Often, it can be ignored.
Suppose a liquid is heated so that its temperature rises by ΔT (very small) and its volume increases from V1 to V2 . Experimentally, it is found that the increase in volume, V2 – V1 , is proportional to V1 and ΔT.
Hence, (V2 – V1 ) α V1 ΔT.
∴ V2 – V1 = β V1 ΔT, where β is a constant of proportionality called the volumetric expansion coefficient of the liquid.
β = \(\cfrac{V_2-V_1}{V_1ΔT}\).
It is expressed in per °C.
We have V2 = V1+ βV1 ΔT = V1 (1 + β ΔT).
β is the increase in the volume of a liquid per unit original volume per unit rise in its temperature.
2. A gas is enclosed in a container. When it is heated at constant pressure, both the container and the gas expand. Suppose a gas is heated at constant pressure so that its temperature rises by ΔT (very small) and its volume increases from V1 to V2 . Experimentally, it is found that the increase in volume, V2 – V1 is proportional to V1 and ΔT. Hence,
(V2 – V1) a V1 ΔT.
∴ V2 – V1 = β V1 ΔT, where β is a constant of proportionality, the volumetric expansion coefficient, called the constant pressure expansion coefficient.
β = \(\cfrac{V_2-V_1}{V_1ΔT}\)
It is expressed in per °C.
We have V2 = V1 + βV1 T = V1 (1 + β ΔT).
β is the increase in the volume of a gas per unit original volume per unit rise in its temperature when the pressure is kept constant.
