Heating and cooling

Themes > Science > Physics > Cryogenics > Temperature > Is a negative Kelvin temperature possible? > Behaviour of the model > Heating and cooling

If heat is added, more and more particles change from the low energy level to the high energy level (note that the levels themselves are unchanged); the number of particle with high energy, N(hi), grows and N(lo) decreases so the logarithm becomes less negative and temperature rises. The energy of the whole ensemble rises because now there are more particles on the high energy level.

Try calculating the temperature for the system shown in picture (two level model), but one particle changed his place from low to high level.

On the other hand, if energy is withdrawn from a body, E(lo), the low energy level, is populated at the cost of E(hi). The value of the logarithm becomes more and more negative

and temperature goes towards zero. Also, from the expression can be concluded that it must be difficult to reach absolute zero, as a diagram of the logarithm versus the ratio shows.

Logarithm function
The logarithm changes much when argument is small.

At low ratio of N(hi)/N(lo) the logarithm is very steep; hence if only a few particles change from low to high, temperature rises appreciably. As can easily be imagined, it is not a simple task to keep some 10²³ particles on the low state; keep in mind that it takes very little energy to rise but a few atoms to the high level.

As can be seen from these examples, the formula behaves as we would expect temperature to behave.