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Escape Velocities of Gases

To escape the Earth's gravity, an object near the top of the atmosphere at an altitude of 100 km must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. The temperature at which gas molecules attain the rms speed, which is equal to the escape velocity, can be estimated by using the equation for the average kinetic energy of the gas molecules. According to the kinetic theory of gas, the average kinetic energy of the gas molecules is proportional to its temperature.
Heating and Cooling Curves02:44

Heating and Cooling Curves

When a substance—isolated from its environment—is subjected to heat changes, corresponding changes in temperature and phase of the substance is observed; this is graphically represented by heating and cooling curves.
For instance, the addition of heat raises the temperature of a solid; the amount of heat absorbed depends on the heat capacity of the solid (q = mcsolidΔT). According to thermochemistry, the relation between the amount of heat absorbed or released by a substance, q, and its...
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Temperature relaxation in hot dense hydrogen.

Michael S Murillo1, M W C Dharma-wardana

  • 1Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. murillo@lanl.gov

Physical Review Letters
|June 4, 2008
PubMed
Summary

Hydrogen temperature equilibration for fusion energy was slower than predicted. New simulations show slower relaxation than Landau-Spitzer, especially at lower temperatures, but agree at high temperatures.

Area of Science:

  • Plasma physics
  • Computational physics

Background:

  • Accurate modeling of hydrogen plasma is crucial for inertial confinement fusion (ICF) research.
  • Existing Landau-Spitzer predictions for temperature equilibration may require refinement under specific ICF conditions.

Purpose of the Study:

  • To investigate the temperature equilibration of hydrogen under ICF-relevant conditions.
  • To compare new simulation results with established theoretical predictions.

Main Methods:

  • Utilizing advanced molecular-dynamics simulations.
  • Employing quantum many-body theory for calculations.
  • Comparing results against Landau-Spitzer predictions across a range of temperatures and densities.

Main Results:

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  • Observed slower temperature relaxation rates than predicted by Landau-Spitzer.
  • Discrepancies persisted even at kilo-electron-volt temperatures.
  • Agreement between simulations and theory was approached in the high-temperature limit.
  • Conclusions:

    • Current Landau-Spitzer predictions may overestimate the speed of temperature equilibration in hydrogen plasmas under certain ICF conditions.
    • Further theoretical and computational work is needed to refine models for ICF applications.
    • High-temperature behavior shows convergence, suggesting validity of models in that regime.