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Chapter 18

Chapter 18. Thermal Properties of Matter. Equations of state. A first model for describing the behavior of a gas is the ideal-gas equation. Active study of gases is done by changing pressure, volume, temperature, or quantity of material and observing the result. Q18.1.

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Chapter 18

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  1. Chapter 18 Thermal Properties of Matter

  2. Equations of state • A first model for describing the behavior of a gas is the ideal-gas equation. • Active study of gases is done by changing pressure, volume, temperature, or quantity of material and observing the result.

  3. Q18.1 A quantity of an ideal gas is contained in a balloon. Initially the gas temperature is 27°C. You double the pressure on the balloon and change the temperature so that the balloon shrinks to one-quarter of its original volume. What is the new temperature of the gas? A. 54°C B. 27°C C. 13.5°C D. –123°C E. –198°C

  4. A18.1 A quantity of an ideal gas is contained in a balloon. Initially the gas temperature is 27°C. You double the pressure on the balloon and change the temperature so that the balloon shrinks to one-quarter of its original volume. What is the new temperature of the gas? A. 54°C B. 27°C C. 13.5°C D. –123°C E. –198°C

  5. Q18.2 p This pV–diagram shows three possible states of a certain amount of an ideal gas. Which state is at the highest temperature? 3 2 1 A. state #1 B. state #2 C. state #3 D. Two of these are tied for highest temperature. E. All three of these are at the same temperature. V O

  6. A18.2 p This pV–diagram shows three possible states of a certain amount of an ideal gas. Which state is at the highest temperature? 3 2 1 A. state #1 B. state #2 C. state #3 D. Two of these are tied for highest temperature. E. All three of these are at the same temperature. V O

  7. Car engine • In automobile engine, a mixture of air and gasoline is compressed in the cylinders before being ignited. A typical engine has a compression ratio of 9.00:1. The initial pressure is 1.00 atm and the initial temperature is 27°C. If pressure after compression is 21.7 atm, find the temperature of the compressed gas.

  8. Solving for the quantity of material given P, V, and T • You add compressed air into a scuba tank which started at 1 atm pressure and want to find out mass of that air. • What do you need to know and what can you assume is constant during this process?

  9. An improvement to the equation of state • The van der Waals equation includes corrections for the facts that molecules are not point particles, that they have volume, and for the attraction/repulsion that naturally exists between the adjacent atoms/moleculesin an ensemble.

  10. Δ(PV) curves at constant temperature—isotherms • A single experiment can measure how pressure changes as volume changes. This is an isothermal curve. • Many isothermal curves together make a three-dimensional phase surface. • How do you predict from these graphs what happens to material in a sealed, rigid container if temperature is increased?

  11. Molecular properties of matter • Just for perspective, the amount of carbon in the graphite of just one #2 pencil represents 1023 carbon atoms. • Each adjacent atom (or molecule) in a sample will experience forces from its “neighbors.” These forces range in strength over several orders of magnitude.

  12. Microscopes can now resolve individual atoms • For centuries, evidence of individual atoms was clever inference from macroscopic measurements. • Scanning or tunneling electron microscopy is now able to resolve objects of atomic and molecular size.

  13. Atomic/molecular collisions and pressure • The kinetic-molecular theory relates pressure to elastic collisions between individual particles and the walls of the container. • Even though atoms/molecules are light, they move at hundreds or even thousands of m/s, and each contributes significant kinetic energy.

  14. Q18.3 Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (vrms) and the average translational kinetic energy per molecule (KE) compare in the two specimens? A. vrms and KE are both greater in specimen #2. B. vrms is greater in specimen #2; KE is the same in both specimens. C. vrms is greater in specimen #2; KE is greater in specimen #1. D. Both vrms and KE are the same in both specimens. E. None of the above is correct.

  15. A18.3 Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (vrms) and the average translational kinetic energy per molecule (KE) compare in the two specimens? A. vrms and KE are both greater in specimen #2. B. vrms is greater in specimen #2; KE is the same in both specimens. C. vrms is greater in specimen #2; KE is greater in specimen #1. D. Both vrms and KE are the same in both specimens. E. None of the above is correct.

  16. Q18.4 Consider two specimens of ideal gas at the same temperature. Specimen #1 has the same total mass as specimen #2, but the molecules in specimen #1 have greater molar mass than the molecules in specimen #2. In which specimen is the total translational kinetic energy of the entire gas greater? A. specimen #1 B. specimen #2 C. The answer depends on the particular mass of gas. D. The answer depends on the particular molar masses. E. Both C. and D. are correct.

  17. A18.4 Consider two specimens of ideal gas at the same temperature. Specimen #1 has the same total mass as specimen #2, but the molecules in specimen #1 have greater molar mass than the molecules in specimen #2. In which specimen is the total translational kinetic energy of the entire gas greater? A. specimen #1 B. specimen #2 C. The answer depends on the particular mass of gas. D. The answer depends on the particular molar masses. E. Both C. and D. are correct.

  18. Speed of air molecules • What is the average translational kinetic energy of one molecule an ideal gas of nitrogen (molar mass M = 32 g/mol) at 27°C? What about oxygen (molar mass M = 28 g/mol)? • What is the rms speed of nitrogen and oxygen?

  19. How much heat energy can ensembles contain? • An atom can absorb energy as the kinetic energy of its motion. • A molecule can absorb energy in its translation, and also in its rotation and in the vibrations of one atom in its structure with respect to the others. • Atomic/molecular energy absorbed is termed its “heat capacity.”

  20. Illustration of heat absorption into degrees of freedom

  21. Measuring atomic/molecular speeds • Beams of molecules are created in a vacuum chamber where the pressure is low enough to have a mean free path at least 10 × farther than the sample path. (A typical apparatus would require 10−6 torr to obtain mean free path ~10–100 m and accommodatea 1 m experimental setup.)

  22. Molecules form distributions of velocities • A temperature-dependent distribution forms around the most likely velocity for a given sample.

  23. The positions of (s), (l), and (g) are plotted on phase diagrams • Lines are drawn for freezing, melting, and boiling curves on a pT axis.

  24. P, V, and T may all be plotted to form 3-D surfaces

  25. P, V, and T may all be plotted to form 3-D surfaces II

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