Experiment 12 CHARLES LAW Objectives 1. To set up a model of thermal machine, 2. To put to work the model to verify Charles law, 3. To describe and explain Charles law Theory (NOTE: This theory is the same that we covered before in Experiment 11on the Ideal Gas model) Thermodynamics is one of the physics branches that, among other things, study the thermal properties of gases. The simplest model that allows explaining how the gases behave is the ideal gas model. The properties of the ideal gas model are described through the general equation of the ideal gas, or equation of state of the gas. This equation establishes a relationship among relevant physical variables such as pressure, p, volume, V, and absolute temperature, T. The equation is valid for any constant mass of gas in thermal equilibrium, that is to say, with a uniform temperature, and it is mathematically expressed as, pv = nrt Where n is the number of moles of gas and R, the molar constant of gases, with a value of J 8.314 mol K, in the International System of units. This equation of state was discovered experimentally analyzing the behavior of the gas, maintaining constant one of the three variables while allowing the other two to change. Real gases do not behave exactly as established by the ideal gas model but they are considered ideal as a first approximation 1. Boyle-Mariotte law relates pressure to volume at constant temperature (isothermal process) in a process where the gas is initially at a pressure p 1 and volume V 1 and ends up at a pressure p 2 and volume V 2, while the temperature remains the same. This is mathematically written as, Example 1 p 1 V 1 = p 2 V 2 We have one liter, l, of air (we will represent liters with letter l) at a pressure p = 1.0 atm, within a cylinder similar to the one of the thermal machine that we will use in this experiment. See Figure 12-1. We apply pressure on the piston of the cylinder until duplicating its original value. The process is carried out at a constant temperature. We want to calculate the final volume of the gas using the ideal gas model Solution: Data: V 1 = 1.0 l, p 1 = 1.0 atm, p 2 = 2p 1 = 2.0 atm, and T 1 = T 2 = constant Unknown: V 2 Equation: V 2 = V 1 (p 1 / p 2 ) = (1.0 l) (1.0 atm/2.0 atm) = ½ l We see that when duplicating the pressure we reduce the volume to a half of its original value, which means that the gas is compressed. The volume of an ideal gas at a constant temperature is inversely proportional to the pressure Exercise 1 We have a mass of gas, at a constant temperature, inside a variable volume cylinder. We move the piston of the cylinder and obtain the values of pressure and volume shown in Table 1. Given the data in that table complete the blanks. Note that we do not allow air to leave or enter the cylinder. (Hint: Boyle-Mariotte law requires the product pv to remain constant in each case) 1
Table 1 No p (atm) V (l) pv (verification) 1 4.0 0.3 2 2.0 3 0.5 4 0.6 2. Charles and Gay-Lussac law, relates volume to temperature at constant pressure (isobaric process) in a process where the gas is initially at an absolute temperature T 1 and volume V 1 and ends up at an absolute temperature T 2 and volume V 2, while the pressure remains the same. This is mathematically written as, Example 2: V1 V2 = T1 T2 We have 0.5 lof H at 20 C. We increase the temperature up to 60 C. Find the volume of the gas at the new temperature if during this process we maintained a constant pressure Solution: Data: V 1 = 0.5 l, t 1 = 20 C, t 2 = 60 C Unknown: V 2 Equation: V 2 = V 1 (T 2 /T 1 ) Before making the corresponding substitutions we must notice that the given temperatures, t 1 and t 2, are expressed in Celsius degrees, or centigrade, and that Charles and Gay-Lussac law refers to absolute temperature, therefore, we must change the temperatures from Celsius degrees to Kelvins. This is done by adding 273.15 to the temperature in Celsius, thus, T 1 = t 1 + 273.15 = 20 + 273.15 = 293.15 K. In the same way, T 2 = t 2 + 273.15 = 60 + 273.15 = 333.15 K, then T2 333.15 K V2 = V1 = (0.5 l) = 0.57 T 1 293.15 K We see that when warming up the gas, its volume increases, if the pressure remains constant Exercise 2: We have a given mass of gas, at a constant pressure, enclosed within a variable volume cylinder. We change the temperature of the gas and obtain the values of the volume shown in Table 2. Observe the data and fill the blanks. Notice that we did not allow changes in the air mass within the cylinder. (Hint: Charles and Gay-Lussac law requires quotient V/T to remain constant in each case) Table 2 No t ( C) V (l) T(K) V/T (verification) 1 70 3.0 2 120 3 5.0 4-40 l 2
3. Finally, when the volume stays constant, while the pressure and temperature change, we obtain a relation that is written as, p1 p2 = T1 T2 Example 3: A constant mass of gas at pressure p 1 = 1.5 atm and temperature t 1 = 50 C is taken to a new temperature t 2 = 200 C at a constant volume. Calculate its new pressure Solution: Data: p 1 = 1.5 atm, t 1 = 50 C, t 2 = 200 C Unknown: p 2 Equation: p 2 = p 1 (T 2 /T 1 ) Before making the corresponding substitutions we must notice that the given temperatures, t 1 and t 2, are expressed in Celsius degrees, or centigrade, and this law requires absolute temperatures, therefore, we must convert Celsius to Kelvins. This is done by adding 273.15 to the temperature in Celsius, thus, T 1 = t 1 + 273.15 = 50 + 273.15 = 323.15 K. In the same way, T 2 = t 2 + 273.15 = 200 + 273.15 = 473.15 Then K, then T2 473.15 K p2 = p1 = 1.5 atm = 2.2 atm T 1 323.15 K We notice that when warming up the gas, its pressure increases if its volume remains constant, Exercise 3: We have a given mass of gas, at a constant volume, inside a cylinder. We change the temperature of the gas and obtain the pressure values of Table 3. Observe the data and fill in the blanks. Notice that we do not allow changing the mass of air within the cylinder. (Hint: the law of constant volume requires quotient p/t to remain unchanged in each case) Table 3 No t ( C) p (atm) T (K) p/t (verification) 1 70 5.0 2 120 3 2.0 4-40 In this laboratory exercise we will use a thermal machine model to measure changes in the volume of air as a function of its temperature. See Figure 12-1. We must notice that the mass of the gas does not change in this process. In the following Internet site there is an animation of the experiment that we are going to carry out in this laboratory session. Go to this WEB site, see the figure and press the button to start the animation. Remember that you must wait a few minutes before the animation runs http://physics.gac.edu/~mellema/aapt2001/charles%27%20law.htm 3
Figure 12-1Apparatus to verify Charles law Materials Thermal machine Pyrex container with hot water Electric heater Ice Empty glass Thermo meter Procedure 1. Check that the equipment of Figure 12-1 and the materials in the previous list are on your laboratory bench 2. Close the metal air chamber with the stopper 3. Connect the air chamber to the thermal machine with a plastic hose 4. Closes the valve of the tube that is not being used in the base of the thermal machine 5. Check that the piston of the thermal machine is resting in the base of the cylinder 6. Lay down the thermal machine on the laboratory bench in such a way that the red scale of the cylinder is upwards 7. Put boiling water in the pyrex glass up to half its volume 8. Introduce the air chamber in the hot water, and wait until the piston moves away from the cylinder s base 9. Read the water temperature and the position of the piston on the red scale of the thermal machine 10. Allow the hot water in the glass to cool down and take the temperature and the piston s position every five degrees. If the process is too slow you can add ice to the hot water 11. Stop the measurements once the piston goes back to the cylinder s bottom 4
Experiment 12 Laboratory report Charles Law Section Laboratory bench number Date: Students: 1. Write the temperatures and positions of the piston in a table. Convert Celsius degree to K (kelvins). Calculate the corresponding volumes for each position of the piston knowing that the diameter of the cylinder is 32.5 mm 5
2. Make a graph of volume versus temperature and add it to your report Conclusions 6
Experiment 12 Questions Charles Law Attention: There is no quiz for this experiment. The grade that you obtained in the Ideal Gas quiz is going to be considered for this experiment. Both experiments have the same quiz, which is taken at the beginning of the Ideal Gas laboratory session 7