Explain about Hope's experiment to demonstrate the anomalous expansion of water
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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
\[\Delta V\,\doteq\,\beta V_0 \Delta t,\tag{1}\]
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):
\[V\,\doteq\,V_0\,+\,\beta V_0 \Delta t\,=\,V_0(1\,+\,\beta\Delta t). \tag{2}\]
Relationship (2) can be expanded using mass and density:
\[\frac{m}{\rho}\,\doteq\,\frac{m}{\rho_0}(1\,+\,\beta\Delta t), \tag{3}\]
which can be simplified to:
\[\rho\,\doteq\,\frac{\rho_0}{1\,+\,\beta\Delta t}.\tag{4}\]
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.
The dependence of (distilled) water on temperature is illustrated by Fig. 1.

Tools
Hope's device, two thermometers (two sensors connected to a computer, which can plot the development of temperature in time; useful, though not necessary. In this experiment, two identical Vernier Go!Temp sensors were used.), crushed ice, kitchen salt, two large beakers (or other containers, preferably 500 ml or bigger).
Hope's device
A simple device demonstrating the anomaly of water was designed in 1805 by Scottish scientist Thomas Charles Hope (1766-1844), among others the discoverer of strontium.
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
\[\Delta V\,\doteq\,\beta V_0 \Delta t,\tag{1}\]
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):
\[V\,\doteq\,V_0\,+\,\beta V_0 \Delta t\,=\,V_0(1\,+\,\beta\Delta t). \tag{2}\]
Relationship (2) can be expanded using mass and density:
\[\frac{m}{\rho}\,\doteq\,\frac{m}{\rho_0}(1\,+\,\beta\Delta t), \tag{3}\]
which can be simplified to:
\[\rho\,\doteq\,\frac{\rho_0}{1\,+\,\beta\Delta t}.\tag{4}\]
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.
The dependence of (distilled) water on temperature is illustrated by Fig. 1.

Tools
Hope's device, two thermometers (two sensors connected to a computer, which can plot the development of temperature in time; useful, though not necessary. In this experiment, two identical Vernier Go!Temp sensors were used.), crushed ice, kitchen salt, two large beakers (or other containers, preferably 500 ml or bigger).
Hope's device
A simple device demonstrating the anomaly of water was designed in 1805 by Scottish scientist Thomas Charles Hope (1766-1844), among others the discoverer of strontium.
Answered by
9
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
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