Now that we have introduced the concept of temperature, we can begin to ask what a change in temperature does to different substances. We will then see that through this study we will obtain a more fundamental temperature scale, the Kelvin scale.
It is easiest to start with gases, for which we can easily measure the so-called thermodynamics variables pressure, p, volume, V, and temperature, T. By enclosing a fixed known amount of gas in a container, it was observed that if one fixes the available volume, the pressure increases linearly with the temperature. Further, it was found that if one works at constant pressure, the temperature is inversely proportional to the available volume. The combination of this type of experimental observations has led to the establishment of the so-called ideal gas law.
Ideal Gas Law:
p V = N k T = n R T or
p1V1/T1 = p2V2/T2 N is the number of molecules in the quantity of gas, and k is called Boltzmann's constant
k = 1.38·10-23 J/K n is the number of moles and R is the ideal gas constant
R = 8.31 J/mol·K = 0.0821 L·atm/mol·K
This relation works extremely well for all gases at low densities and most gases at normal densities. Only at high densities do we have to take higher order effects into account, such as the fact that individual gas molecules have their own volume that other molecules cannot get into. Then the ideal gas law's approximations break down. Needless to say that this is beyond the scope of this course.
Special cases:
By fixing any one of the thermodynamic variables at a constant value,we arrive at these following special cases of the ideal gas law:
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