Thermodynamics is essentially how heat energy transfers from one substance to another.
In “Joe Science vs. the Water Heater,” the temperature of water in a water heater must be found without measuring the water directly from the water heater. This problem was translated to the lab by providing heated water, fish bowl thermometers, styrofoam cups, and all other instruments found in the lab. The thermometer only reaches 45 degrees celsius; therefore, thermodynamic equations need to be applied in order to find the original temperature of the hot water. We also had access to deionized water that was approximately room temperature. Two equations were used in this experiment to determine the initial temperature of the hot water.
The first equation was that the q value of the hot water is equal to the negative q value of the cool deionized water. This is shows as equation 1. The next equation was that the q value of a reaction is equal to the product of mass, specific heat, and change in temperature. This is shown in equation 2. (1)(2)Equation 2 can be substituted into Equation 1, creating the expression showed here:(3)The method used for this experiment is as follows. First, 100 mL of regular deionized water was measured using a 100 mL graduated cylinder.
This water was then poured into the styrofoam cup that will be used to gather the hot water later. The water level was then marked using a pen on the inside of the cup. The water was then dumped out, and the cup was dried. Next, 100 mL of regular deionized water was measured using a 100 mL graduated cylinder, and the fish tank thermometer was placed in the water.
Once the temperature was stabilizing in the graduated cylinder, the marked styrofoam cup was filled to the mark with hot water. Quickly, the temperature of the regular water was recorded immediately before it was poured into the styrofoam cup. The regular/hot water was mixed for a couple seconds, and the fish tank thermometer was then submerged into the water. After approximately 30 seconds, the temperature of the mixture leveled out, and was recorded. This was repeated three times. Referring back to Equation 3, mass and specific heat can be cancelled out.
This is by using the same mass and realizing that the specific heat of both the regular water and the hot water are the same. In our procedure, 100 mL of hot water was mixed with 100 mL of the regular water; therefore, the masses in Equation 3 cancel out (the densities of the water at different temperatures aren’t exactly the same, but the difference is negligible). This leads to the change in temperature of the hot water equaling the negative change of temperature in the regular water, shown as: (4)Using Equation 4, it can be inferred that the initial temperature of the hot water minus the change in temperature of the mixture equals the temperature of the cold water plus the change in temperature of the mixture (Equation 5). This is then rearranged to indicate that the initial temperature of the hot water is two times the change in temperature plus the initial temperature of the regular water.
This is shown in Equation 6. (5)(6)This is the equation used in finding the initial temperature of the hot water by plugging in our recorded values. For each trial, the temperature of the regular water was 23, 24, and 25 degrees celsius respectively, and the change in temperature was 18, 18, and 17 degrees respectively. By plugging these values into Equation 6, the temperature of the hot water was 59, 60, and 59 degrees celsius. From the results, the temperature of the hot water would be 59 degrees celsius. This number is not very precise; although, it does serve its purpose.
Also, there are many different advantages and disadvantages to the method used as opposed to others. The disadvantage is the imprecise measurement of the 100 mL of hot water. It was measured using a drawn line on the inside of the cup, and this is less precise than the measurement of the volume of hot water using a graduated cylinder. The main advantage of this method is the containment of the hot water. Since the hot water stays in the styrofoam cup from start to finish, very little heat energy is lost. This is better than transferring the hot water to glassware because it would lose heat much faster.
Also, since the same mass was used for both kinds of water, the computation of the temperature was much easier. The mass cancelled out as well as the specific heat in Equation 3. With the advantages and disadvantages stated, the main cause of error for this would be the measurement of 100 mL of hot water. There are also forms of human error that can occur. This includes misreadings of temperatures and measurements of volume. Overall, this method produced a fairly repeatable outcome that was approximately 59 degrees celsius.
The results of this method are accurate; however, this value is not precise. Despite this, the precision serves for Joe Science’s purpose of knowing the temperature of his water heater.