Question

what is the importance anamolous behaviour of water by using hopes apparatus

Answer 1

The goal of this experiment is to demonstrate that between the temperatures 0 °C and 4 °C, the density of water increases with increasing temperature. (To be exact: we are going to demonstrate that water has a higher density at 4 °C than at 0 °C.)

Theory: thermal volume expansion of liquids

The volume of liquids is, similarly to solids and gases, dependant on their current temperature. Liquids (with the exception described below) increase their volume with increasing temperature; the increase of their volume ΔV is, with some neglect, directly proportionate to increase of temperature Δt and the initial volume V0. This relation can be mathematically denoted as

ΔV≐βV0Δt,(1)

(1)ΔV≐βV0Δt,

where the constant β describes the volumetric thermal expansion coefficient and is a characteristic property of every liquid. (The neglect mentioned above limits the validity of this relationship to “small” differences in temperature, where βΔt≪1.). The volume of the liquid V after heating is therefore equal to the sum of its initial volume Vo and the growth ΔV given by relationship (1):

V≐V0+βV0Δt=V0(1+βΔt).(2)

(2)V≐V0+βV0Δt=V0(1+βΔt).

Relationship (2) can be expanded using mass and density:

mρ≐mρ0(1+βΔt),(3)

(3)mρ≐mρ0(1+βΔt),

which can be simplified to:

ρ≐ρ01+βΔt.(4)

(4)ρ≐ρ01+βΔt.

The result is logical and predictable – if the volume of a liquid increases with increasing temperature, its density (while conserving mass) necessarily decreases.

Theory: anomaly of water

The constant β used in the relationships above is itself dependent on temperature; this dependence is usually very small. In the case of water, however, β has negative values in the narrow range between 0 °C and 4 °C. Heating water inside this interval therefore leads to a decrease in volume, or an increase in density. This phenomenon, unobserved in other liquids, is often referred to as the anomaly of water.

The volume of water is then apparently minimal (and the density maximal) at approx. 4 °C; exceeding this temperature leads to the values of β becoming positive again and a subsequent increase in temperature causes an increase in volume (decrease in density), in agreement with the general theory.

Answer 2

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