## Microscopic Versus Macroscopic

We can analyse any system on different scales. We can either analyse the system as a whole, or we can analyse the system in terms of it's components on the smallest scale.

The first is called the macroscopic scale. Macroscopic measurements – temperature, weight etc – can often be made directly, but microscopic measurements are usually very small, and must be measured indirectly. Often a macroscopic quantity is an average of the microscopic equivalents.

Possibly the best example of the differences between macroscopic and microscopic scale is in measuring temperature.

The internal or heat energy of 1 mol of an ideal gas is given by

whereBoltzmann's constant and T is the absolute temperature in K (Kelvins).

The kinetic energy of an individual molecule of massand speedisIf the motion of the gas molecules is random, then the average kinetic energy is directly related to the absolute temperature:

The temperature and the average kinetic energy are macroscopic quantities. The average kinetic energy though is averaged over all the kinetic energies of the molecules of the gas, each one of which is a microscopic quantity.

Pressure too exists in the same sense. Pressure is force per unit area. When the molecules of a gas in a container hit the sides of the container, they bounce off and their momentum changes, resulting in a force being exerted on the walls of the container. Summing all these changes of momentum, each of which is a microscopic quantity, in each second, results in a macroscopic quantity. Each individual molecule exerts a pressure, but only the pressure exerted by the gas as a whole can be properly measured.

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