Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...

In multivariable calculus, a function of two variables can exhibit local maximum or minimum values at certain points on its surface. A local maximum occurs when the function's value at a point is greater than at all nearby points, while a local minimum occurs when the function’s value is less than at all nearby locations. These points are referred to as local extrema and are of central importance in optimization problems.Local extrema are found at critical points, where the surface becomes...

Van de Graaff generators (or Van de Graaffs) are devices used to demonstrate high voltage due to static electricity that can also be used for research. Robert Van de Graaff first built one in 1931 (based on original suggestions by Lord Kelvin) for use in nuclear physics research.
Van de Graaff uses both smooth and pointed surfaces, conductors, and insulators to generate large static charges and, hence, large voltages. A substantial excess charge can be deposited on the sphere because it moves...

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...