Thermodynamics

=**Thermodynamics - Heat Exchange - Calorimetry (AP Physics: B Final Project)**=

**Heat Exchange Between Water and Glass Experiment**

 * John Ticknor**

=**Purpose.**=

The purpose of this experiment is to demonstrate the process of the conservation of energy. This surrounds components of thermodynamic concepts. In addition, the quantities of specific heat capacities will also be considered in depth. We wish to identify in this experiment the amount of time required for a heated beaker of water that is transferred into a separate glass beaker initially at room temperature to reach thermal equilibrium. This is the common final temperature of the water within the glass.

**Procedure.**
In this experiment, we obtain the initial materials. They include two 250 mL glass beakers, a hot plate, a mass scale, distilled water, a stopwatch, and a digital temperature sensor.



We find the mass of the desired reception container. This will be the glass beaker that will obtain the heated water. Our glass beaker maintained a mass of 100.0 grams. We transfer 150 mL of distilled water initially at room temperature (22.6 °C) into a glass beaker. We then placed the glass beaker on the hot plate set for a medium heat magnitude. We placed the temperature sensor within the water that was being heated. We allowed the temperature of the heated water to reach approximately 50.0 °C. Once this temperature was reached, we immediately removed the temperature sensor and placed it within the glass beaker that was initially at room temperature of a measured 23.5 °C. We quickly poured the heated water into the glass beaker attempting to minimize any heat exchange to the surroundings at this time. We started the stopwatch at this time and measured the temperature of the heated water within the glass in six 20 second intervals for 240 seconds (4 minutes).

The mass of the receiving beaker measured to be approximately 100.0 grams.

The experimental process where the water is heated to the ending temperature of 50.0 °C and subsequently added to the receiving container on the right. The temperature was placed first into the beaker and then the heated water was added. Immediately after the water was added, we started to the stopwatch to record the time. The photo below demonstrates this.



**Analysis and Results.**
We employed the following equation for the purposes of this experimental process:

//heat lost by the water = heat gained by the glass//
This can be further expanded to include the following factors that determine the quantity of heat energy for a given system:

//Q = mC∆T//
For the parameters of this experiment, we expand this equation as follows:

//**= (Mass of the Glass Beaker) * (Specific Heat of Glass) * (Change in Temperature of the Glass)**//
Abbreviated as such:



In order to obtain the mass of the water, a critical factor, we must calculate it through the known density and volume of the water.



In this case, we calculate:

//mass of the water = (150 cm^3) * (1.0*10^3 kg/m^3) = (1.5*10^-4 m^3) * (1.0*10^3 kg/m^3) = 0.15 kilograms//
We are aware of the following known specific heat capacities:


 * Specific Heat for Water = 4186 J / kg * °C (Joules per kilogram Celsius)**
 * Specific Heat for Glass = 840 J / kg * °C (Joules per kilogram Celsius)**

We now maintain all required quantity factors required for calculation of the common final temperature that exists in thermal equilibrium.

We employ the following equation to calculate the final equilibrium temperature. In this case, we expand the change in temperature to include the following quantities:

T­0 = initial temperature of the heated water (left) T­0 = initial temperature of the glass with no water (right) T­F = final equilibrium temperature when the water is transferred to the glass container



By substituting known values, we obtain:



By performing the necessary equation manipulation to isolate the singe unknown variable of TF, we obtain:



We obtained a table of data that consists of the time elapsed since the water was added to the beaker initially at room temperature and the temperatures at each corresponding time:


 * t (s) || TF (°C) ||
 * 0 || 50.0 ||
 * 20 || 49.3 ||
 * 40 || 49.0 ||
 * 60 || 48.6 ||
 * 80 || 48.4 ||
 * 100 || 48.0 ||
 * 120 || 47.8 ||
 * 140 || 47.5 ||
 * 160 || 47.2 ||
 * 180 || 47.0 ||
 * 200 || 46.7 ||
 * 220 || 46.5 ||
 * 240 || 46.2 ||



Given that the final predicted temperature for thermal equilibrium where the heat gained by the glass is equal to that of the heat lost by the water is approximately 46.9 °C, the amount of time elapsed required to reach this temperature was experimentally found to be between 180 and 200 seconds. This final result assumes several conditions, however. We assumed that all of the heat lost by the water was directly transferred to the glass, which is likely not the case. Given that the glass was not enclosed within a calorimeter to contain all released heat, the data may be somewhat inaccurate due to this. A major improvement would have to do with enclosing the glass beaker within a calorimeter to better seal off the system. This might provide better readings in terms of data and a more measurable final equilibrium temperature. This could allow us to predict the specific heat of the glass beaker, and this scenario we assumed it to be a specific value.