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]: The Soave equation adds an acentric factor to this statement, and the virial equation measures deviations from this law using a compressibility factor. This law derived by Benoit Clapeyron can account for density in its "dirty mop" form, and when A and B terms are added to account for the volume and interactions between particles, it is called van der Waals equation. Containing a namesake constant that is Boltzmann's constant times Avogadro's number is, for 10 points, what law usually stated as PV equals nRT
[EX A]: Science

[EX Q]: The attenuated total reflection type of this can be used on compounds with a low surface area, while the diffuse reflectance type can be used to study samples that are not sufficiently transparent. The multiplex advantage explains the use of the Fourier Transform type of this. Diatomic bonds are generally not found in the fingerprint region, and the stretching seen using this technique generally occurs at higher frequencies than the bending. Most types of this use some sort of absorption, because each bond in the molecule will absorb only its characteristic frequency. For 10 points, name this type of analytical technique, which categorizes compounds based on the frequency of the vibration of its bonds when exposed to radiation of waves longer than those of visible light.
[EX A]: Science

[EX Q]: Euler's proof of Fermat's Last Theorem for the n equals 3 case involved extending integer arithmetic to one of these structures, which contain numbers of the form a plus b times the square root of negative 3. Dedekind defined an ideal complex number based upon a property related to these structures and Hilbert utilized (*) polynomial ones to solve his Basis Theorem. The advent of quaternion algebra and the extension of the axioms of this structure to square matrices led to the formulation of its non-commutative theory and the first single theory of the abstract commutative variety of these structures was proposed by Noether. FTP, what are these mathematical objects defined as a set containing two operators that satisfy a collection of axioms.
[EX A]:
Science