State the three observations made in Hope’s experiment.
Answers
Explanation:
experiment
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)
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)
Relationship (2) can be expanded using mass and density:
mρ≐mρ0(1+βΔt),(3)
which can be simplified to:
ρ≐ρ01+βΔt.(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.
Fig. 1: Temperature dependance of desity of distilled water
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. The picture below (Fig. 2) is taken from Wikipedia.
Obr. 2: Thomas Charles Hope
The body of the device (Fig. 3) consists of a hollow cylinder, which is filled with water and allows two thermometers to be inserted at different heights through two holes on the side. In the half of its height, the cylinder is fitted with an outside reservoir for a cooling mixture. This reservoir is in no way connected to the inside of the cylinder.
Obr. 3: Hope's device from side (to the left) a from above (to the right)
Procedure
At least one hour before conducting the experiment, we fill one beaker with water and put it into a fridge. We do the same with an empty Hope's device. This way, we will precool the necessary parts of the experiment.
Right before the experiment itself, we prepare the cooling mixture using crushed ice and kitchen salt; the procedure is described in detail in the experiment Cooling Mixture of Water, Ice and Salt. It is appropriate to have a thermometer to control the temperature of the mixture.
After a thorough cooling we take Hope's device out of the fridge, isolate it from the pad (e.g. with a styrofoam plate) and insert the thermometers into both holes.
We pour the precooled water into the inner cylinder. The thermometers should now show the same temperature. If a measurement in time is available, we start it now.
Now we fill the reservoir with the cooling mixture (Fig. 4). After that we simply observe the development of temperatures measured by both thermometers.
Fig. 4: Layout of the experiment
Sample result
The experiment results in two dependencies of temperature of water in the inner cylinder on time (Fig. 5), blue for the upper thermometer (t1) and red for the lower thermometer (t2). Let us now analyze their shape.
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