4/23/2024 0 Comments Atomic molecular theory![]() The speed of a helium atom changes from one instant to the next, so that at any instant, there is a small, but nonzero chance that the speed is greater than the escape speed and the molecule escapes from Earth’s gravitational pull. The reason for the loss of helium atoms is that there are a small number of helium atoms with speeds higher than Earth’s escape velocity even at normal temperatures. ![]() Very few helium atoms are left in the atmosphere, but there were many when the atmosphere was formed. This temperature is much higher than atmospheric temperature, which is approximately 250 K ( – 25 º C ( – 25 º C or – 10 º F ) – 10 º F ) at high altitude. The speed of sound increases with temperature and is greater in gases with small molecular masses, such as helium. The faster the rms speed of air molecules, the faster that sound vibrations can be transferred through the air. The high value for rms speed is reflected in the speed of sound, however, which is about 340 m/s at room temperature. The mean free path (the distance a molecule can move on average between collisions) of molecules in air is very small, and so the molecules move rapidly but do not get very far in a second. These large molecular velocities do not yield macroscopic movement of air, since the molecules move in all directions with equal likelihood. The rms velocity of the nitrogen molecule is surprisingly large. The kinetic energy is very small compared to macroscopic energies, so that we do not feel when an air molecule is hitting our skin. The average translational kinetic energy depends only on absolute temperature. Note that the average kinetic energy of the molecule is independent of the type of molecule. ![]() This assumption is not always valid, but the same result is obtained with a more detailed description of the molecule’s exchange of energy and momentum with the wall. We also assume the wall is rigid and that the molecule’s direction changes, but that its speed remains constant (and hence its kinetic energy and the magnitude of its momentum remain constant as well). We assume that a molecule is small compared with the separation of molecules in the gas, and that its interaction with other molecules can be ignored. Calculating the average force exerted by such molecules will lead us to the ideal gas law, and to the connection between temperature and molecular kinetic energy. The figure shows an expanded view of an elastic collision of a gas molecule with the wall of a container. But why should increasing the temperature of the gas increase the pressure in the box? A look at the atomic and molecular scale gives us some answers, and an alternative expression for the ideal gas law. ![]() We know from our previous discussions that putting more gas into the box produces greater pressure, and that increasing the temperature of the gas also produces a greater pressure. Figure 13.21 shows a box filled with a gas. ![]()
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