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Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. [2] [3] It is named after Friedrich Paschen who discovered it empirically in 1889. [4]
Liquid hydrogen (H 2 (l)) is the liquid state of the element hydrogen. Hydrogen is found naturally in the molecular H 2 form. [4] To exist as a liquid, H 2 must be cooled below its critical point of 33 K. However, for it to be in a fully liquid state at atmospheric pressure, H 2 needs to be cooled to 20.28 K (−252.87 °C; −423.17 °F). [5]
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The enthalpy of reaction can then be analyzed by applying Hess' law, which states that the sum of the enthalpy changes for a number of individual reaction steps equals the enthalpy change of the overall reaction.
For an ideal gas the equation of state can be written as =, where R is the ideal gas constant.The differential change of the chemical potential between two states of slightly different pressures but equal temperature (i.e., dT = 0) is given by = = = , where ln p is the natural logarithm of p.
The lifting power in air of hydrogen and helium can be calculated using the theory of buoyancy. The buoyancy depends upon the difference of the densities (ρ air) − (ρ gas) rather than upon their ratios. The lifting force for a volume of gas is given by the equation: F B = (ρ air - ρ gas) × g × V
The energy or temperature to induce release affects the cost of any chemical storage strategy. If the hydrogen is bound too weakly, the pressure needed for regeneration is high, thereby cancelling any energy savings. The target for onboard hydrogen fuel systems is roughly <100 °C for release and <700 bar for recharge (20–60 kJ/mol H 2). [13]
To absorb hydrogen, the dehydrated form of LOHC (an unsaturated, mostly aromatic compound) reacts with the hydrogen in a hydrogenation reaction. The hydrogenation is an exothermic reaction and is carried out at elevated pressures (approx. 30-50 bar) and temperatures of approx. 150-200°C in the presence of a catalyst.