Ideal Gas Law – Macroscopic Perspective

1. Ideal Gas Law – Macroscopic Perspective • Course level • Introductory chemistry/physics course • Where we are in the course • Developed mechanical tools such as Newton’s second law and the concept of work. • Covered first law of thermodynamics and the concepts of internal energy, work, and heat transfer. • Recently discussed microscopic model of an ideal gas and how internal energy is related to the temperature. • Introduced last class.

2. Ideal Gas Law: Macroscopic Perspective Outline/Introduction • Quick Pre-Test • Start to get you thinking about this topic, but don’t worry, we are going to re-take the quiz at the end of class! • Projects • In small groups, you will work through short “projects” that work through a different misconception about gases • Post-Test • The post test will revisit the pre-test questions, plus some new ones, that exemplify the ideas learned in the projects

3. Pretest Question #1 A syringe that contains an ideal gas and has a frictionless piston of mass M is moved from an ice-water bath to a beaker of boiling water, where it comes to thermal equilibrium. Will the pressure and volume of the gas increase, decrease, or remain the same?

4. Pretest Question #2 • Three identical cylinders are filled with unknown quantities of ideal gases. The cylinders are closed with identical frictionless pistons of mass M. Cylinders A and B are in thermal equilibrium with the room at 20 °C, and cylinder C is kept at a temperature of 80 °C. • Cylinders A and B: • PA > PB • PA < PB • PA = PB • Cylinders B and C: • PB > PC • PB < PC • PB = PC

5. Pretest Question #3 • A cylinder with a frictionless piston contains an ideal gas. The cylinder is placed in an insulating jacket and small masses are added. • Will the pressure, temperature, and volume of the gas increase, decrease, or remain the same?

6. Ideal Gas Law – Macroscopic Perspective • Learning Goals • Understand the relationship of pressure, temperature, and volume in an ideal gas from a macroscopic perspective, with emphasis on addressing common misconceptions. • Learning Objectives • Think critically about the appropriate use of the ideal gas law and tie in concepts learned earlier in the course. • Relate gas pressure to mechanical equilibrium using free-body diagrams. • Interpret hypothetical situations involving pressure, temperature, and volume (more than two variables). • Develop an ability to foster scientific discussion about the macroscopic properties of gases.

7. Group project #1Relating gas pressure and mechanical equilibrium Force Pressure: Cross-sectional area = Atmospheric pressure • Draw a free-body diagram for a frictionless piston of mass that seals a gas-filled cylinder. • Come up with an expression for the pressure of the gas using Newton’s second law.

8. Group project #1Relating gas pressure and mechanical equilibrium Force Pressure: Cross-sectional area = Atmospheric pressure piston by gas piston by Earth piston by atmosphere

9. Group project #2Relating gas pressure and mechanical equilibrium Cylinder A Cylinder B • PA > PB? • PA < PB? • PA = PB? • Explain.

10. Group project #2Relating gas pressure and mechanical equilibrium Cylinder A Cylinder B • PA = PBbecause both pistons have the same mass and the same atmospheric force acted upon them piston by gas piston by Earth piston by atmosphere

11. Group project #3Internal energy, work, heat transfer Change in internal energy of the system: Heat transferred to the system Work done by the system • In what direction does the piston need to move such that ? • (Think of the analogy of a block on an incline plane.)

12. Group project #3Internal energy, work, heat transfer Change in internal energy of the system: Heat transferred to the system Work done by the system • For W>0, the gas, i.e. system, must do work. Work is defined as W = F*Dd (force times distance), and for a gas, W=p*DV. Therefore, for W>0,DV>0, or the piston moving up . The internal energy of the gas is proportional to its temperature, and increasing the temperature would increase the volume (at constant pressure).

13. Group project #4Internal energy, work, heat transfer Change in internal energy of the system: Heat transferred to the system Work done by the system • Thermally insulated cylinder. How would the piston have to move in order for the temperature to increase?

14. Group project #4Internal energy, work, heat transfer Change in internal energy of the system: Heat transferred to the system Work done by the system • Thermally insulated cylinder. Because the piston is insulated, there is no heat transfer. For the temperature to go up, work must be done on the gas, and the piston must be pushed down.

15. Post-test Question #1 A syringe that contains an ideal gas and has a frictionless piston of mass M is moved from an ice-water bath to a beaker of boiling water, where it comes to thermal equilibrium. Will the pressure and volume of the gas increase, decrease, or remain the same?

16. Post-test Question #1 • PRESSURE REMAINS THE SAME • Forces exerted by the atmosphere and gravitational force on the piston are the same in the ice water as in the boiling water • VOLUME INCREASES • Since the pressure is the same in the initial and final states, from the ideal gas law, the increase in temperature is associated with an increase in volume

17. Post-test Question #2 • Three identical cylinders are filled with unknown quantities of ideal gases. The cylinders are closed with identical frictionless pistons of mass M. Cylinders A and B are in thermal equilibrium with the room at 20 °C, and cylinder C is kept at a temperature of 80 °C. • Cylinders A and B: • PA > PB • PA < PB • PA = PB • Cylinders B and C: • PB > PC • PB < PC • PB = PC

18. Post-test Question #2 • PA = PB • The pressures in Cylinder A and B are equal because the atmospheric pressure and weight of the piston are the same • PB= PC • Similar to above, the free-body diagram would show no difference between Cylinder B and Cylinder C, therefore the pressure of the gases are the same

19. Post-test Question #3 • A cylinder with a frictionless piston contains an ideal gas. The cylinder is placed in an insulating jacket and small masses are added. • Will the pressure, temperature, and volume of the gas increase, decrease, or remain the same?

20. Post-test Question #3 • Temperature Increases • Positive work is done on the gas; the cylinder is insulated so there is little or no heat transfer, therefore by 1st law of thermodynamics, the internal energy of the gas increases, and internal energy is proportional to temperature. • Volume Decreases • In the final position, the piston will be lower than the initial state, so a decrease in volume • Pressure Increases • Because the system of piston and masses has a greater weight than before and it at rest, the pressure increases

21. Post-Test Question #4 • A cylinder is divided into two chambers by a freely sliding piston of mass M. In each of the situations, both chambers contain unknown amounts of ideal gases and the piston is at rest. Both gases are at the same temperature. • Compare the pressures of the gases in the two chambers.

22. Post-Test Question #4 • In the double-chamber with different volumes, the pressures are the same • In the double-chamber with different gases, the pressures are the same • In both scenarios, the pressures are the same on both sides because cylinders are horizontal and the sliding piston is at rest

23. Post-Test Question #2 • Two identical cylinders with frictionless pistons contain an equal number of moles of the same ideal gas at the same pressure. Cylinder 1 has a piston of mass M. In the bottom diagram are three movable pistons of different masses that fit cylinder 2. • Choose the correct piston for cylinder 2 such that P1 = P2.

24. Post-Test Question #2 • Piston B • Piston B is correct because it needs to have the same mass as the piston in cylinder 1 to balance out the same forces • Also, because both cylinders contain the same number of moles, the volume of the sample in cylinder 2 is greater

25. Summary • Common misconceptions addressed • Incorrectly assume that P is always proportional to 1/V • Incorrectly assume that P is always proportional to T • Incorrectly relating gas pressure to mechanical equilibrium • Incorrectly relating gas pressure to a microscopic model • Physics education research results Kautz et al. Am. J. Phys., 73, 1005 (2005) & Kautz et al. Am. J. Phys., 73, 1064 (2005)