Peoples Physics Book Version-2

http://www.ck12.org Chapter 20. Gas Laws

FIGURE 20.5

Diagrams of the same process on different axes

Question

explain how we can draw the graph of the processes on the left on aP−Vdiagram.

Answer

During steps 1-2, the gas’s temperature is linearly proportional to its volume; therefore, by the combined ideal

gas law, the pressure must remain constant while the volume increases. During steps 2-3, the volume remains

constant, so by Gay-Lussac’s law, pressure must increase linearly with temperature. Finally, during steps 3-

4, volume falls linearly with increases in temperature. In other words,V=a−bTfor some constantsa,b.

Plugging in forTfrom the combined ideal gas law, we find that pressure is inversely proportional to volume

(derive the formula); that is, as volume decreases linearly, pressure grows along a hyperbola.

An Ideal Gas Thermometer, Absolute Zero

Finally, let’s look at the ideal gas law [7] for 1 mole of some gas that doesn’t deviate from the law, like helium gas,
for instance:

PV=RT 1 mole of ideal gas

This formula (alternatively, we could have used Charles’ Law), combined with the idea of the perfectly elastic
balloon above, suggests a way to measure temperature: at constant pressure, the volume of the balloon should be
directly proportional to its temperature, with the slope of the line equal to the ratio of the ideal gas constant and the
constant pressure. That is,