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Chapter Analysis
Intermediate13 pages • EnglishQuick Summary
The chapter introduces the kinetic theory of gases, explaining the behavior of gases based on molecular motion. It discusses the ideal gas equation, pressure, volume, and temperature relationships. The theory provides insights into concepts such as the mean free path, viscosity, and diffusion, highlighting the connection between macroscopic and microscopic properties of gases.
Key Topics
- •Ideal gas equation
- •Pressure, volume, and temperature relationships
- •Kinetic interpretation of temperature
- •Mean free path
- •Law of equipartition of energy
- •Specific heat capacity
Learning Objectives
- ✓Understand how molecular motion explains gas behavior
- ✓Calculate the pressure of a gas using kinetic theory
- ✓Interpret the kinetic basis of temperature
- ✓Determine mean free path of gas molecules
- ✓Apply the law of equipartition of energy to explain specific heats
Questions in Chapter
Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 Å.
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Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure. Show that it is 22.4 litres.
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What does the dotted plot in Figure 12.8 signify? Which is true: T1 > T2 or T1 < T2?
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An air bubble of volume 1.0 cm³ rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
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Additional Practice Questions
What is the kinetic interpretation of temperature?
mediumAnswer: The kinetic interpretation of temperature states that the temperature of a gas is a measure of the average kinetic energy of its molecules. It is directly proportional to the average energy of the molecular motion.
How does the kinetic theory of gases describe pressure?
mediumAnswer: According to kinetic theory, the pressure exerted by a gas on the walls of its container is due to collisions of the gas molecules with the walls. The pressure is proportional to the average kinetic energy of the molecules.
Explain the concept of mean free path.
hardAnswer: The mean free path is the average distance that a molecule travels between two successive collisions. It depends on the number density and diameter of the molecules.
What is the significance of the law of equipartition of energy?
mediumAnswer: The law of equipartition of energy states that energy is distributed equally among all degrees of freedom of the molecules. For each degree of freedom, the energy is ½ kBT per molecule.
Why does the temperature of a gas not depend on its pressure or volume?
mediumAnswer: In an ideal gas, temperature is solely a measure of the average kinetic energy of the molecules and is independent of pressure and volume. According to kinetic theory, internal energy is related only to temperature.