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Engineering and Scientific Calculations
Published in David E. Clough, Steven C. Chapra, Introduction to Engineering and Scientific Computing with Python, 2023
David E. Clough, Steven C. Chapra
There are common constants used in calculations in chemistry, physics and engineering. One of these is the universal gas constant, R. This constant is employed to relate amount, temperature, pressure, and volume of a gas and appears in the ideal gas law as PV=nRT
Gases and Gas Laws
Published in Kathleen E. Murphy, Thermodynamics Problem Solving in Physical Chemistry, 2020
1.4 If Z = 0.8808 for CH4(g) at 50°C and 130 atm, What is the density of the gas, assuming that it obeyed the ideal gas laws?What is the actual density of the gas?
Gases
Published in W. John Rankin, Chemical Thermodynamics, 2019
An ideal gas is a hypothetical gas defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular forces. It can be visualised as a set of perfectly hard spheres which can collide but which otherwise do not interact with each other. All the internal energy* of such a gas is in the form of kinetic energy (due to the movement of atoms or molecules), and any change in internal energy is thus accompanied by a change in temperature. The ideal gas concept is useful because ideal gases obey the ideal gas law and are amenable to analysis using statistical mechanics. Gases that deviate from ideal behaviour are known as real gases. Though the ideal gas is a hypothetical concept, in many situations many common gases approach ideal behaviour, and ideal behaviour can be assumed in many situations without introducing significant errors.
The limits of Riemann solutions to the relativistic van der Waals fluid
Published in Applicable Analysis, 2021
It is well known that, as stated in [5–7], the ideal gas law indeed relies on such the assumption that gases are composed of point masses that undergo perfectly elastic collisions. However, at a low temperature or high pressure, most of the gases hardly behave like the ideal gas and the behaviors of them deviate from the ideal gas law. Therefore, searching for some realistic gases following a law that fits better with the behavior of gases in usage than the ideal gas becomes extremely urgent. In fact, the behavior of gases with high temperature and pressure in compressible fluids generally follows the van der Waals type non-ideal gas law that deals with the possible real gas effects.
Sensitivity to luminosity, centrifugal force, and boundary conditions in spherical shell convection
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
P. J. Käpylä, F. A. Gent, N. Olspert, M. J. Käpylä, A. Brandenburg
Our simulation setup is similar to that used in Käpylä et al. (2019) with a few variations that will be explained in detail. We solve a set of fully compressible hydromagnetics equations where is the magnetic vector potential, is the velocity, is the magnetic field, η is the magnetic diffusivity, is the permeability of vacuum, is the current density, is the advective time derivative, ρ is the density, ν is the kinematic viscosity, p is the pressure, and s is the specific entropy with , where and are the specific heats at constant volume and pressure, respectively. The gas is assumed to obey the ideal gas law, , where is the gas constant. The rate of strain tensor is given by where the semicolons refer to covariant derivatives (Mitra et al.2009). The acceleration due to gravity, and the Coriolis and centrifugal forces are given by where N m2 kg−2 is the universal gravitational constant, kg is the solar mass, is the angular velocity vector, where is the rotation rate of the frame of reference, is the radial coordinate, and the corresponding radial unit vector. The parameter is used to control the magnitude of the centrifugal force.