Take help of your teachers to make a working model of Hope's apparatus and perform the experiment.
Verify the result you obtain
Answers
The purpose of this experiment is to demonstrate that between 0 °C and 4 °C, the density of water increases with increasing temperature.
That is to say, we are to demonstrate that water has a higher density at 4 °C than at 0 °C.
Theory: thermal expansion of liquids:
The volume of liquids is, dependant on their current temperature. Liquids increase their volume with increasing temperature. The increase of their volume ΔV is, is, directly proportionate to increase of temperature Δt and the initial volume V0.
This relation can be mathematically indicated as :\[\Delta V\,\doteq\,\beta V_0 \Delta t,\tag{1}\]where the constant β is the coefficient of volumetric thermal expansion and is a characteristic property of every liquid.
The volume V after heating it becomes equal to the sum of its initial volume Vo and the increase in volume, 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 by means of mass and density:\[\frac{m}{\rho}\,\doteq\,\frac{m}{\rho_0}(1\,+\,\beta\Delta t), \tag{3}\]:On simplification, \[\rho\,\doteq\,\frac{\rho_0}{1\,+\,\beta\Delta t}.\tag{4}\]:
Thus the result is logical and predictable – if the volume of a liquid increases with increasing temperature, its density necessarily decreases.