Density of Water in the Neighborhood of 4ºC
The object of this experiment is to obtain the density of water in the neighborhood of 4°C. Density is a thermodynamic property.
In this experiment we find the density of water in the neighborhood of 4°C with a sensitive cylindrical float whose diameter is only 1.25 mm at the water line. From 0°C to 4°C(water density is maximum at 4°C) the float rises about 8 mm and from 4°C to 25°C the float sinks about 40 mm. Careful consideration is given to the volumetric change in the float as a function of temperature. When you reduce the data provided you will see how close your density curve follows the curvature of the published density curve shown in Figure 1.1.
Figure 1.1The density of water in the neighborhood of 4°C from Gebhart, et. al. .
The unique property of water, where its maximum density peaks at about 4°C, is the cause of important and interesting physical phenomenon, including thermal inversion of lakes . Noting this maximum density phenomenon Count Rumford  read the following at the Institut de France in 1805:“Judging from the constant temperature which is found at all seasons at the bottom of deep lakes and from the results of several direct experiments, we may conclude that water is at its maximum density when it is at the temperature of about 41° of Fahrenheit’s scale, which corresponds to 4° on that of Reaumur, and to 5° of the Centigrade scale.”
One of Rumford’s experiments is shown inFigure 1.2. Cylindrical vessel A is filled with water and contains brass cup B inside of which smaller, wax-coated, cork cup C supports the bulb of mercurial thermometer D with curved stem. Earthen basin E contains crushed ice. A solid ball of tin F, removed from a bath maintained at 42°F (5.55°C) rests on an opening in tin cover GH. The cone-shaped tip of tin ball F is submerged below the waterlevel in vessel A. The water in vessel A is at 0°C due to the vessel’s submersion in the crushed ice. The 5.55°C cone-shaped tip of tin ball F heats the 0°C water and immediately the density increases (see Figure 1.1) and the water sinks vertically down and is collected in cork cup C. This process continues and results in the cork cup retaining the water with the maximum density, whosetemperature is registered by the thermometer held by the cup. Rumford’s thermometer registered 5°C, but his thermometer was off by a degree – the temperature should be 4°C.
Figure 1.2 Rumford’s apparatus for determining the temperature of the maximum density of water. Sketch is from Rumsford .
I designed a float resembling a commercial,weighted-bulb hydrometer. The float is shown in Figure 1.3 and has three components: a stem, a body, and a ballast. The body is a 15.8mm diameter brass tube with brass disks soldered on both ends. Soldered to the top of the body is a 1.25mm diameter stainless steel stem and at the bottom of the body, extended from a stiff wire, is the ballast made of solder. The body provides the majority of thebuoyancy. The ballast keeps the float vertical and is trimmed (solder added or removed) such that the stem pierces the water surface. The slenderness of the stem provides the float with a vertically sensitive water line.
Figure 1.3 The cylindrical float.
The float was placed in a stainless-steel vacuum bottle that contained water at uniformtemperature – see Figure 1.4. The water temperature was easily varied by the addition of either chilled or warmed water from an outside source. After agitation the temperature remained uniform as indicated by two submerged thermocouples, one located near the water surface and the other near the bottom of the vacuum bottle.
The water line location on the float stem was determined by careful,...