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Schwarzschild's criterion sanjdiâr-e Schwarzschild Fr.: critère de Schwarzschild The condition in stellar interior under which →
ad and rad stand for adiabatic and radiative respectively.
This condition can also be expressed as: ∇_{ad}<∇_{rad},
where ∇ = d lnT / d lnP =
P dT / T dP with T and P denoting temperature and
pressure respectively.
More explicitly, in order for convection to occur the adiabatic temperature gradient
should be smaller than the actual temperature gradient of the surrounding gas,
which is given by the radiative temperature gradient if convection does not occur.
Suppose a hotter → convective cell or
gas bubble rises accidentally by a small distance in height. It gets into a layer
with a lower gas pressure and therefore expands. Without any
heat exchange with the surrounding medium it expands and cools
adiabatically. If during this rise and → adiabatic
expansion the change in temperature is smaller than in the medium the gas
bubble remains hotter than the medium. The expansion of the
gas bubble, adjusting to the pressure of the medium, happens very fast, with the
speed of sound. It is therefore assumed that the pressure in the gas bubble and in the
surroundings is the same and therefore the higher temperature gas
bubble will have a lower density than the surrounding gas. The
→ buoyancy force
will therefore accelerate it upward. This always occurs
if the adiabatic change of temperature during expansion is smaller than the change of temperature
with gas pressure in the surroundings. It is assumed that
the mean molecular weight is the same in the rising bubble and the medium.
See also → Ledoux's criterion;
→ mixing length.Named after Karl Schwarzschild (1873-1916), German mathematical physicist
(1906 Göttinger Nachrichten No 1, 41); → |