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13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
The definitions of pressure and temperature have been developed.
Pressure is the force divided by the area on which it is exerted, and temperature is the force divided by the area.
A better understanding of pressure and temperature can be gained from the theory of gases, which assumes that atoms and molecules are in random motion.
The component of the molecule's momentum that is parallel to the wall is reversed.
The force on the wall creates pressure.
The elastic collision of a gas molecule with the wall of a container is shown in Figure 13.20.
An average force per unit area is observed because a huge number of molecules collide with the wall in a short time.
The source of pressure in a gas is the collision.
The gas pressure is higher if the average is higher.
The relationship is derived from the Things Great and Small feature.
There is a relationship between temperature and the average energy of the molecule in the gas.
We know from previous discussions that increasing the temperature of the gas also increases the pressure in the box.
An alternative expression for the ideal gas law can be found at the atomic and molecular scale.
The figure shows an expanded view of a collision between a gas molecule and a container.
The ideal gas law and the connection between temperature and energy will be determined by the average force exerted by such molecules.
We assume that a molecule is small compared to the separation of molecule in the gas, and that its interaction with other molecule can be ignored.
We assume that the wall is rigid and that the molecule's direction changes, but that its speed remains constant.
The same result can be obtained with a more detailed description of the molecule's exchange of energy and momentum with the wall.
The pressure on the walls of the box is caused by gas in it.
A molecule colliding with a wall has its direction reversed.
The wall has a direction that is parallel to it.
There is no force parallel to the wall because the components of its velocity momentum are not changed.
The change in momentum is.
There is no force between the wall and the molecule.
The force between the molecule and wall is large during the short time of the collision.
The force we are looking for is the average time between the collisions of the molecule with the wall.
It would take the molecule a long time to go across the box and back.
The force is due to one molecule.
The force 13.47 is the average value of the bar over a quantity.
The force should be based on the speed, rather than the component of the speed.
The result is given by this.
The ideal gas law is expressed in this equation.
We can get the average energy of a molecule from the right-hand side of the equation.
The result of this calculation is that the average energy of a molecule is related to the temperature.
The equation has been found to be valid for gases and accurate in liquids.
Another definition of temperature is based on the expression of the energy.
The temperature is known in the equation.
We need to convert the given temperature tokelvins before substituting values.
The temperature is enough to find the average energy.
The average energy of the molecule is not related to the type of molecule.
The average is dependent on absolute temperature.
When an air molecule hits our skin, we don't feel it because the energy is very small.
The nitrogen molecule has a large rms velocity.
The air does not move due to the large molecular velocities.
The mean free path of a molecule in air is very small, and so they don't get very far in a second.
The high value for rms speed is reflected in the sound's speed, which is about 340 m/s at room temperature.
Sound can be transferred through the air at a faster rate if the rms speed of air is faster.
The speed of sound increases with the temperature.
The theory of gases was developed by Daniel Bernoulli, who is best known for his work on fluid flow.
The atomistic view of matter was established by Dalton.
The motion of a molecule in a gas is random in magnitude and direction, but it has a predictable distribution of speeds.
The originators of the distribution were the first to calculate it based on the theory.
The distribution has a long tail because a few Molecules may go several times the rms speed.
The rms speed is the most probable speed.
The rms speed is the most likely speed.
Only a small percentage of the molecule have speeds that are greater than.
The distribution of thermal speeds is dependent on temperature.
The distribution is broadened as the temperature increases.
The distribution is shifted to higher speeds at higher temperatures.
If a person has a high temperature, they are more likely to lose water from their lungs and mouth, which causes a dry sensation in the mouth.
In order to escape Earth's gravity, an object near the top of the atmosphere must travel away from Earth at a rate of over 11 km/s.
The escape velocity is the speed at which you can escape.
Determine which equations to use to solve the problem by identifying the knowns and unknowns.
The escape velocity is 11.1 km/s.
We need to identify the unknowns.
The mass of the atom needs to be solved.
Determine which equations are needed.
The Boltzmann constant is the mass of a helium atom.
Plug the known values into the equations.
The temperature is much higher than the atmospheric temperature.
There were many helium atoms when the atmosphere was formed.
There are a small number of helium atoms with speeds that are higher than Earth's escape velocity.
There is a small chance that the speed of the molecule will be greater than the escape speed, because the speed of the atom changes from one instant to the next.
Oxygen, nitrogen, and water have smaller rms speeds, and so it is less likely that they will have speeds greater than the escape velocity.
Billions of years are required to lose significant amounts of the atmosphere because few have speeds above the escape velocity.
The Moon has lost most of its atmosphere because of its weaker pull.
Problems and Exercises discuss the comparison between Earth and the Moon.
The photograph of Eugene Cernan driving the lunar rover on the moon in 1972 looks like it was taken at night.
The light is coming from the sun.
The Moon's escape velocity is 1/6 that of Earth because of the low acceleration due to gravity.
The Moon has no atmosphere because gas molecules escape very easily.
The sky is black during the day because there is no gas to scatter sunlight.
The number of atoms and molecules hitting the surface of a grain of pollen in a gas is relatively small.
Since the number of atoms and molecules in a gas is immense, the fluctuations are a tiny percentage of the number of collisions, and the averages spoken of in this section vary imperceptibly.
The fluctuations are proportional to the inverse square root of the number of crashes so they can be significant for small bodies.
The Brownian effect was observed for pollen grains in water in the 19th century.
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