1. Unit 6 : Part 2 Temperature and Kinetic Theory

2. Outline Temperature and Heat The Celsius and Fahrenheit Temperature Scales Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale Thermal Expansion The Kinetic Theory of Gases Kinetic Theory, Diatomic Gases, and the Equipartition Theorem

3. Temperature and Heat Temperature is a measure of relative hotness or coldness. Heat is the net energy transferred from one object to another due to a temperature difference. This energy may contribute to the total internal energy of the object, or it may do work, or both.

4. Temperature and Heat

5. A higher temperature does not necessarily mean that one object has more internal energy than another; the size of the object matters as well. When heat is transferred from one object to another, they are said to be in thermal contact. Two objects in thermal contact without heat transfer are in thermal equilibrium.

6. The Celsius and Fahrenheit Temperature Scales A thermometer is used to measure temperature; it must take advantage of some property that depends on temperature. A common one is thermal expansion.

7. The Celsius and Fahrenheit Temperature Scales In everyday use, temperature is measured in the Fahrenheit or Celsius scale. To convert from one to the other:

8. Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale When the temperature of an ideal gas is held constant, When the pressure is held constant,

9. Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale Combining gives the ideal gas law: or with Boltzmann’s constant: N is the total number of molecules in the gas.

10. Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale The ideal gas law can also be written where n is the number of moles of gas and R is the universal gas constant: A mole of a substance contains Avogadro’s number of molecules:

11. Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale A constant-volume gas thermometer is useful because the temperature is directly proportional to the pressure. If P-T curves are plotted for different gases, they converge at zero pressure.

12. Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale The temperature at which this occurs is called absolute zero—no lower temperature is possible. The Kelvin temperature scale has the same increments as the Celsius scale, but has its zero at absolute zero.

13. Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale The three temperature scales are shown here. In physics calculations, the Kelvin temperature scale is used. The Kelvin scale is also called the absolute scale, as the Kelvin temperature is proportional to the internal energy.

14. Thermal Expansion Most materials expand when heated. For small changes in temperature, the change in length is proportional to the change in temperature.

15. Thermal Expansion The changes in area and in volume can be derived from the change in length.

16. Thermal Expansion

17. Water behaves nonlinearly near its freezing point—it actually expands as it cools. This is why ice floats, and why frozen containers may burst.

18. Kinetic Theory of Gases According to the kinetic theory of gases, pressure is due to elastic collisions of molecules with container walls.

19. Kinetic Theory of Gases Using the kinetic theory, it can be shown that The mass and speed are those of an individual molecule. The molecular kinetic energy can be related to the temperature:

20. Kinetic Theory of Gases The internal energy of a monatomic gas is due to the kinetic energy of its atoms, and is therefore related to its temperature.

21. Kinetic Theory of Gases The kinetic theory of gases also helps us understand diffusion as a result of the motion of molecules.

22. Kinetic Theory, Diatomic Gases, and the Equipartition Theorem The atoms in a monatomic gas have only translational equilibrium to contribute to the internal energy. A diatomic molecule can also rotate around two distinct axes ( x and y ).

23. Kinetic Theory, Diatomic Gases, and the Equipartition Theorem The equipartition theorem tells us what the contribution of the rotational states is to the internal energy. A diatomic molecule has 5 degrees of freedom—translation in x, y, or z, rotation around x, and rotation around y.

24. Kinetic Theory, Diatomic Gases, and the Equipartition Theorem The predicted internal energy of a diatomic gas is then:

25. Summary Celsius–Fahrenheit conversions: Heat is the energy transferred from one object to another due to temperature difference.

26. Summary Ideal gas law: Absolute zero is –273.15°C. Celsius–Kelvin conversion:

27. Summary Thermal expansion: Results of kinetic theory of gases: (monatomic gas) (diatomic gas)