Dr. Aaron Titus | Department of Physics, High Point University PHY1050      Astronomy of Stars, Galaxies, and the Cosmos home | WebAssign | textbook | course calendar

## kinetic energy

The temperature of the lowest part of the corona is 2 million kelvins. Yet the chromosphere is only 7,000 to 15,000 kelvins. How can the less dense and much larger corona have a much higher temperature than the chromosphere or even the photosphere?

This is a subject of ongoing research. The process by which ions (atoms stripped of some of their electrons) are accelerated to achieve such high temperatures in the corona is not well understood. However, let's at least understand how temperature is related to the motion of atoms in a gas.

The temperature of a gas is proportional to the average kinetic energy of an atom in the gas. The higher the temperature, the greater the average kinetic energy of an atom. The proportion can be written

Kinetic energy is energy of motion. For speeds less than about 10% of the speed of light, the average kinetic energy of an atom in the gas is equal to

Thus, the higher the temperature of the gas, the faster on average the atoms will move. In fact, the speed of an atom is proportional to the square root of the temperature. We call this the rms speed because it's the square root of the average of v2 for the atoms in the gas.

If the temperature of a gas is doubled, by what factor does the average kinetic energy of an atom in the gas increase?

If the temperature of a gas is doubled, by what factor does the rms speed of an atom in the gas increase?

The simulation below shows 50 atoms in a container. You can change the temperature of the gas in order to see its effect on the motion of the atoms.

Note that the density of air at standard conditions is such that 50 atoms would occupy a box one millionth of a centimeter on a side.

The temperature indicated for the gas is in kelvins, but the kinetic energy and speed are in arbitrary units.

Click the PLAY button to play the animation at a temperature of 100 kelvins. You can change the temperature using the slider. You can also click the links to view the gas with different temperatures.

Do all of the atoms in the gas have the same speed?

The density of the corona is very low, only about a billionth of the density of air at the surface of Earth. However, the particles are moving very fast, such that the temperature of the corona can reach 2 million kelvin. Remember that high temperature for a gas just means that the atoms are moving very fast. The mechanism that accelerates atoms to such high speeds in the corona is not well understood as far as I know.

## A note on temperature scales

In the US, we are accustomed to measuring temperatures in Fahrenheit degrees. However, most countries in the world use celsius degrees. Furthermore, the SI unit for temperature is the kelvin (K).

A kelvin and a celsius degree are the same. However, the zero point for the kelvin scale is different than the zero point for the celsius scale. Zero kelvins is absolute zero. It is physically impossible to cool matter to zero kelvin. Zero kelvin is at -273 °C. Thus, a temperature in degrees celsius is just the temperature in kelvins plus 273.

At high temperatures like a million kelvin, subtracting 273 doesn't change the number very miuch. Thus, you can think of kelvins and celsius degrees as being synonymous for very high temperatures such as those of the photosphere, chromosphere, and corona of Sun.

The freezing point of water is 0 °C and the boiling point of water is 100 °C.

The Fahrenheit scale is defined such that the freezing point of water is 32°F and the boiling point of water is 212 °F.

Temperatures in celsius can be converted to Fahrenheit using

T (in °F) = T(in °C)*9/5 + 32

Temperatures in Fahrenheit can be converted to Celsius using

T (in °C) = 5/9 * (T(in °F) - 32)

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