In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

[EX Q]: After allying with the khan of Chagatai and taking part in campaigns in Transoxania, this ruler would lose a "muddy battle" against Ilyas Khodja, despite fighting alongside brother-in-law Husayn of Balkh. Becoming the head of the Barlas upon the death of Tughluk, this man annihilated Tokhtamysh and the Golden Horde at the Battle of the Terek River before he overwhelmed Sultan Mehmud's forces in seizing the Delhi Sultanate. Prior to his death and ultimate succession by Shah Rukh while planning an invasion of China, he defeated the Turks at the Battle of Ankara and captured Bayezid I. FTP, name this Mongol military leader who ruled in Central Asia during the 14th century from his capital of Samarkand.
[EX A]: History

[EX Q]: The Clausius-Clapeyron equation assumes the change in this to be zero. Because this quantity is most useful when the substance in question is both isothermal and isobaric, a different quantity is used for explosive substances. An equation partially due to the namesake of this quantity gives the temperature dependence of this quantity for an ideal gas. A zero change in this quantity for a system implies that the system is in equilibrium, but a negative value for this quantity implies that a reaction is spontaneous. One may derive this by utilizing the Legendre transform on the internal energy of a system. For ten points, name this state function named for its American inventor, which measures the maximum amount of work attainable from a system, defined as enthalpy minus the product of temperature and entropy.
[EX A]: Science

[EX Q]: The Curtin-Hammett principle states that product ratios are based on transition state ratios and not this conformation value. The rate constant is related to this value by the Brnsted relation and its temperature dependence is given by the (*) van't Hoff equation. It can be obtained from activities through the law of mass action. The natural logarithm of this value times the gas constant and temperature yields the standard Gibbs energy change of a reaction. For 10 points, name this constant that changes according to Le Chatelier's principle.
[EX A]:
Science