pv = nrt Where n is the number of moles of gas and R, the molar constant of gases, with a value of

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1 Experiment 11 IDEAL GAS Objectives 1. To set up a thermal machine laboratory model, 2. To raise an object of a given mass using the thermal machine model, and 3. To describe and explain the operation of the thermal machine model Theory 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 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, p 1 V 1 = p 2 V 2 Example 1 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 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 Figure 11-1(a) thermal Machine (b) Components of the thermal machine 2.

2 Table 1 No p (atm) V (l) pv (verification) Figure 11-1(a) thermal Machine (b) Components of the thermal machine 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, V1 V2 = T1 T2 Example 2: 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 2

3 temperature, therefore, we must change the temperatures from Celsius degrees to Kelvins. This is done by adding to the temperature in Celsius, thus, T 1 = t = = K. In the same way, T 2 = t = = K, then T K V2 = V1 = (0.5 l) = 0.57 T 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) l 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 to the temperature in Celsius, thus, T 1 = t = = K. In the same way, T 2 = t = = Then K, then T K p2 = p1 = 1.5 atm = 2.2 atm T 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 3

4 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) In this laboratory exercise we will use a model of a thermal machine to study the change in volume of air as a function of temperature. Also we will discover that these changes of volume, in combination with two valves, allow the thermal machine to do work. We must notice that the mass of gas changes in this process. See Figure There is an animation of the experiment that we are going to perform in this laboratory session. See the following Internet link: See Figure 5 at this Web site. Place the cursor of the mouse on this figure to initiate the video clip. Remember that you will have to wait for a few minutes to download the video before it runs Materials Thermal machine Mass of 100 g Polystyrene container with hot water Polystyrene container with cold water Procedure 1. Check that your laboratory bench has the equipment shown in the Figure 11-1together with the materials that appear in the previous list 2. Be sure that the piston of the thermal machine is resting in the base of the cylinder 3. Place a weight of 100 g on the piston of the thermal machine 4. Introduce the air chamber in the container that has hot water in it. Wait until the piston raises 5. Withdraw the air chamber of the hot water and put it into cold water. Wait for the air to enter the chamber 6. Repeat steps 4 and 5 until the piston reaches its full extension Notice that the procedure follows that seen in the video clip 4

5 Experiment 11 Laboratory report Ideal Gas Section Laboratory bench number Date: Students: 1. Calculate the work done by the thermal machine to lift the 100 g weight 2. Explain in detail how the thermal machine works. Describe the operation of the valves 3. Where does the energy that lifts the 100 g mass come from? 5

6 Conclusions 6

7 Experiment 11 Questions Ideal Gas This questionnaire has some typical questions on experiment 11. All students who are taking the laboratory course of University Physics I must be able to correctly answer it before trying to make the experiment 1. Thermodynamics is one of the physics branches that, among other things, studies: a. The behavior of valves b. Angular moment c. Linear moment d. The causes of motion e. The properties of gases 2. The simplest model that allows to study how gases behave is: a. A thermal machine b. Charles and Gay-Lussac law c. The molar constant of gases d. Boyle-Mariotte law e. The ideal gas 3. The properties of the ideal gas are described by means of: a. Its internal energy b. The intermolecular force c. The pressure d. Its equation of state e. The law of conservation of mass 4. Boyle-Mariotte law is applied to processes where: a. The mass of the gas and its temperature do not change b. The mass of the gas changes but its temperature remains constant c. The mass of the gas and its volume do not change d. The mass, temperature, pressure and volume change e. The mass of the gas and its pressure do not change 5. Charles and Gay-Lussac law applies to processes where: a. The mass of the gas and its temperature do not change b. The mass of the gas changes but its temperature remains constant c. The mass of the gas and its volume do not change d. The mass, temperature, pressure and volume change e. The mass of the gas and its pressure do not change 6. Let have a mass of gas, at a constant temperature, inside a cylinder with a variable volume. The initial gas pressure is 1.5 atm with a volume of 0.4 l. We change the cylinder volume until obtaining a new pressure of 0.5 atm. The new gas volume is: a. The same b. Reduced to a third of his original value c. 1.2 l d. We need to know the air mass e. We need to know the gas temperature 7. Let have a mass of gas at constant temperature, inside a cylinder of variable volume. The initial gas pressure is 2.5 atm with a volume of 1.2 l. We move the piston to obtain a new volume of 0.5 l. The new gas pressure is: a. We need to know the gas temperature b. The same c. We need to know the gas mass d atm 7

8 e. 6.0 atm 8. Let have a mass of gas at a constant pressure, inside a variable volume cylinder. The initial gas temperature is 90 C with a volume of 300 cm 3. We increase the gas temperature to 180 C. Its new volume is: a. 374 cm3 b. Double the original one because the temperature doubled c. We need to know the pressure value d. We need to know the gas mass e. We need to know to equivalence between cubical centimeters and liters 9. Let have a mass of gas at a constant pressure, inside a variable volume cylinder. The initial temperature of the gas is 50 C, with a volume, of 100 cm 3. We warm up the gas, and its volume increases up to 200 cm 3. The new gas temperature is: a. 100 C b. The double of the original one because the volume duplicated c. 173 C d. We need to know the gas pressure e. We need to apply the law of thermal machines 10. Let have constant mass of gas at a pressure of 12.0 atm and 500 C temperature. We reduce its temperature to 200 C at a constant volume. Its new pressure is: a. Smaller temperature means larger pressure b. 4.8 atm c. 30 atm d. 7.3 atm e. We need to know the gas volume 11. Assuming the ideal gas model complete the following table by filling the blanks: No. Initial values Final values p (atm) V (l) t ( C) T (K) p (atm) V (l) t ( C) T (K) To receive partial credit include all calculations that lead to the results 8

Theory (NOTE: This theory is the same that we covered before in Experiment 11on the Ideal Gas model)

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