Ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur–Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma. The classical thermodynamic properties of an ideal gas can be described by two equations of state: The ideal gas law is the equation of state for an ideal gas, given by: where The ideal gas law is an extension of experimentally discovered gas laws. It can also be derived from microscopic considerations. Real fluids at low density and
Negative number the rules of signs for expanding the multiplication formula_3, and al-Karaji wrote in his "al-Fakhrī" that "negative quantities must be counted as terms". In the 10th century, Abū al-Wafā' al-Būzjānī considered debts as negative numbers in "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen". By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve polynomial divisions. As al-Samaw'al writes: the product of a negative number — "al-nāqiṣ" — by a positive number — "al-zāʾid" — is negative, and by a negative number is positive.