Kinetic theory of gases in cylinder

In summary, the conversation discusses two gas cylinders containing identical masses of monatomic gases, argon and radon. The pressures in both cylinders are equal, but the temperatures differ. The question is posed to determine the ratio of average kinetic energy between a radon atom and an argon atom. The kinetic theory is mentioned, with the formula P V = \frac{2}{3} E for monatomic ideal gases, as a means to approach the problem.
  • #1
abstrkt
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Two gas cylinders are identical. One contains the monatomic gas argon (Ar), and the other contains an equal mass of the monatomic gas radon (Rn). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio KEAvg,radon / KEAvg,argon of the average kinetic energy of a radon atom to the average kinetic energy of a argon atom.

I was thinking since P = NMV^2/3L^3 to set that equal to each other for the same pressure, but I am lost on how to approach it from there. Any help will be appreciated. Thanks.
 
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  • #2
From the kinetic theory we have [tex] P V = \frac{2}{3} E [/tex] for monatomic ideal gases (a pretty good approximation for the noble gases). The answer is one step way.
 

What is the kinetic theory of gases?

The kinetic theory of gases is a scientific model that explains the behavior and properties of gases at the molecular level. It states that gases are composed of tiny particles called molecules that are in constant motion and have negligible volume compared to the volume of the gas.

What is the relationship between temperature and kinetic energy in the kinetic theory of gases?

According to the kinetic theory of gases, the temperature of a gas is directly proportional to the average kinetic energy of its molecules. This means that as the temperature of a gas increases, the average speed and energy of its molecules also increase.

What is the ideal gas law and how does it relate to the kinetic theory of gases?

The ideal gas law is a mathematical equation that describes the relationship between pressure, volume, temperature, and number of moles of an ideal gas. It is derived from the kinetic theory of gases, which assumes that gases behave ideally when the molecules are far apart and do not interact with each other.

How does the kinetic theory of gases explain the different states of matter?

The kinetic theory of gases states that the state of matter of a substance is determined by the strength of the intermolecular forces between its molecules. In gases, the molecules have weak intermolecular forces, allowing them to move freely and independently. In liquids, the forces are stronger, causing the molecules to be more closely packed together. In solids, the forces are even stronger, resulting in a rigid and closely packed arrangement of molecules.

What factors affect the behavior of gases according to the kinetic theory of gases?

The behavior of gases is affected by several factors, including temperature, pressure, and volume. An increase in temperature or a decrease in pressure will result in an increase in the average kinetic energy and speed of the gas molecules. A decrease in volume will cause the molecules to collide more frequently, resulting in an increase in pressure.

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