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Thermodynamics

# Thermodynamics - Thermodynamics Now let us turn our...

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Thermodynamics Now let us turn our attention to gases. If we compress a gas while keeping its temperature constant, we find that the pressure increases as the volume decreases. The rate of increase in pressure is inversely proportional to the decrease in volume, so that pV = constant (21.1) This is called Boyle's law . This is true for all gases at low densities. But it had been found that the absolute temperature of a gas at low densities is proportional to the pressure at constant volume. Similarly, the absolute temperature (i.e. the temperature in Kelvin) is proportional to the volume of a gas if the pressure is kept constant. Thus at low densities, the product pV is approximately proportional to the temperature T pV = CT where C is a constant of proportionality. In order to determine the constant, consider two containers, each holding the same amount of gas at the same temperature. If each container has a volume V , then when we combine the two containers, the resulting new container has a volume of 2 V , yet the pressure and temperature remain unchanged. Thus C must be proportional to the number of molecules in the gas, pV = NkT (21.2) where k is called Boltzmann's constant . It has a value of k = 1.381x10 -23 J/K Ideal Gas Law Measuring the number of molecules in a gas is extremely difficult. It is much easier to measure the mass of the gas and convert over to the number of moles in the gas. A mole (mol) of any substance is the amount of that substance that contains Avogadro's number of atoms or molecules. Avogadro's number is defined as the number of carbon atoms in 12 g of 12 C. It has a value of N A = 6.022x10 23 molecules/mol. If we have n moles of a substance, the number of molecules is N = nN A Thus (21.2) becomes

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pV nN kT nRT A = = (21.3) This is known as the ideal gas law . Here R is called the universal gas constant , and it has a value of R = 8.314 J/mol-K. The mass of 1 mol is called the molar mass M . The molar mass of 12 C is 12 g/mol. Thus the mass of n moles of gas is given by m = nM . So we see that the number of moles in the gas can be determined by knowing the chemical composition and measuring the mass of the gas. The ideal gas law is an example of an equation of state . If the amount of gas is constant, then the state of the gas is determined by any two of
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Thermodynamics - Thermodynamics Now let us turn our...

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