of proportionality. We can see that this constant is proportional to the amount of gas by considering the following. Suppose that we have two containers with identical volumes, each holding the same amount of the same kind of gas at the same temperature and pressure. If we consider the two containers as one system, we have twice the amount of gas at twice the volume, but at the same temperature and pressure. We have thus doubled the quantity PV/T=C by doubling the amount of gas. We can therefore write C as a constant k times the number of molecules in the gas NC=k N Eq.(9-1) then becomesPV=N kT (9-2) The constant k is called Boltzmann's constant. It is found experimentally to have the same value for any kind of gask=1.381×10-23J/K=8.617×10-5eV/K(9-3) An amount of gas is often expressed in moles. A mole (mol) of any substance is the amount of that substance that contains Avogadro's number NA of atoms or molecules, defined as the number of carbon atoms in 12 g of C12NA=6.022×1023 (9-4) If we have ν moles of a substance, then the number of molecules isN=νNA(9-5)Eq.(9-2) is thenPV=νNAkT=νRT (9-6)where R=NAk is called the universal gas constant. Its value, which is the same for all gases, is R=NAk=8.314J/(mol·K)=0.08206L·atm/(mol·K)(9-7) An ideal gas is defined as one for which PV/(νT) is constant for all pressures. The pressure, volume, and temperature of an ideal gas are related by PV=νRT (9-8) Eq.(9-8), which relates the variables P, V, and T, is known as the ideal-gas law, and is an example of an equation of state. It describes the properties of real gases with low densities (and therefore low pressures). At higher densities, corrections must be made to this equation. For any gas at any density, there is an equation of state relating P, V, and T for a given amount of gas. Thus the state of a given amount of gas is determined by any two of the three state variables P, V, and T.
The temperature 0℃ and the pressure of 1 atm are often referred to as standard conditions. Under standard conditions, a mol of an ideal gas occupies a volume of 22.4L.
For a fixed amount of gas, we can see from Eq.(9-8) that the quantity PV/T is constant. Using the subscripts 1 for the initial values and 2 for the final values, we have
P2V2T2=P1V1T1(9-9)Glossary temperature 温度
hotness热
coldness冷
the zeroth law of
thermodynamics
热力学第零定律
ideal-gas temperature scale
理想气体温标
universal gas constant普适气体常量
Boltzmann's constant玻尔兹曼常量
mole摩尔
Avogadro's numbe