This expression is consistent with Boyle’s law (pV = constant) when n and T are
constant, with both forms of Charles’s law (p ∝ T, V ∝ T) when n and either V or p
are held constant, and with Avogadro’s principle (V ∝ n) when p and T are constant.
The constant of proportionality, which is found experimentally to be the same for
all gases, is denoted R and called the gas constant. The resulting expression
pV = nRT (1.8)°
is the perfect gas law (or perfect gas equation of state). It is the approximate equation of
state of any gas, and becomes increasingly exact as the pressure of the gas approaches
zero. A gas that obeys eqn 1.8 exactly under all conditions is called a perfect gas (or
ideal gas). A real gas, an actual gas, behaves more like a perfect gas the lower the pressure,
and is described exactly by eqn 1.8 in the limit of p → 0. The gas constant R
can be determined by evaluating R = pV/nT for a gas in the limit of zero pressure
(to guarantee that it is behaving perfectly). However, a more accurate value can be
obtained by measuring the speed of sound in a low-pressure gas (argon is used in
practice) and extrapolating its value to zero pressure. Table 1.2 lists the values of R in
a variety of units.
The surface in Fig. 1.8 is a plot of the pressure of a fixed amount of perfect gas
against its volume and thermodynamic temperature as given by eqn 1.8. The surface
depicts the only possible states of a perfect gas: the gas cannot exist in states that do not
correspond to points on the surface. The graphs in Figs. 1.4, 1.6, and 1.7 correspond
to the sections through the surface (Fig. 1.9).
This expression is consistent with Boyle’s law (pV = constant) when n and T areconstant, with both forms of Charles’s law (p ∝ T, V ∝ T) when n and either V or pare held constant, and with Avogadro’s principle (V ∝ n) when p and T are constant.The constant of proportionality, which is found experimentally to be the same forall gases, is denoted R and called the gas constant. The resulting expressionpV = nRT (1.8)°is the perfect gas law (or perfect gas equation of state). It is the approximate equation ofstate of any gas, and becomes increasingly exact as the pressure of the gas approacheszero. A gas that obeys eqn 1.8 exactly under all conditions is called a perfect gas (orideal gas). A real gas, an actual gas, behaves more like a perfect gas the lower the pressure,and is described exactly by eqn 1.8 in the limit of p → 0. The gas constant Rcan be determined by evaluating R = pV/nT for a gas in the limit of zero pressure(to guarantee that it is behaving perfectly). However, a more accurate value can beobtained by measuring the speed of sound in a low-pressure gas (argon is used inpractice) and extrapolating its value to zero pressure. Table 1.2 lists the values of R ina variety of units.The surface in Fig. 1.8 is a plot of the pressure of a fixed amount of perfect gasagainst its volume and thermodynamic temperature as given by eqn 1.8. The surfacedepicts the only possible states of a perfect gas: the gas cannot exist in states that do notcorrespond to points on the surface. The graphs in Figs. 1.4, 1.6, and 1.7 correspondto the sections through the surface (Fig. 1.9).
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