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The Rüchardt experiment, [1] [2] [3] invented by Eduard Rüchardt, is a famous experiment in thermodynamics, which determines the ratio of the molar heat capacities of a gas, i.e. the ratio of (heat capacity at constant pressure) and (heat capacity at constant volume) and is denoted by (gamma, for ideal gas) or (kappa, isentropic exponent, for real gas).
For example, a steel block with a volume of 1 cubic meter might expand to 1.002 cubic meters when the temperature is raised by 50 K. This is an expansion of 0.2%. If a block of steel has a volume of 2 cubic meters, then under the same conditions, it would expand to 2.004 cubic meters, again an expansion of 0.2%.
In the first, constant-volume case (locked piston), there is no external motion, and thus no mechanical work is done on the atmosphere; C V is used. In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case.
This is a derivation to obtain an expression for for an ideal gas. An ideal gas has the equation of state: = where P = pressure V = volume n = number of moles R = universal gas constant T = temperature. The ideal gas equation of state can be arranged to give:
In thermodynamics, the Volume Correction Factor (VCF), also known as Correction for the effect of Temperature on Liquid (CTL), is a standardized computed factor used to correct for the thermal expansion of fluids, primarily, liquid hydrocarbons at various temperatures and densities. [1]
It is empirically true that this volume is about 0.26V c (where V c is the volume at the critical point). This approximation is quite good for many small, non-polar compounds – the value ranges between about 0.24V c and 0.28V c. [12] In order for the equation to provide a good approximation of volume at high pressures, it had to be ...
It is easy to verify that for an ideal gas defined by suitable microscopic postulates that αT = 1, so the temperature change of such an ideal gas at a Joule–Thomson expansion is zero. For such an ideal gas, this theoretical result implies that: The internal energy of a fixed mass of an ideal gas depends only on its temperature (not pressure ...
The attenuation coefficient of a volume, denoted μ, is defined as [6] =, where Φ e is the radiant flux;; z is the path length of the beam.; Note that for an attenuation coefficient which does not vary with z, this equation is solved along a line from =0 to as: