In: Physics
Isolated molecular clouds can have a temperature as low as 20 K and a particle density as great as 1.2×105 per cubic centimeter.
What is the minimum mass that a cloud with these properties needs in order to form a star?
Mcloud= _________ MSun
GIVEN:
The temperature of the molecular clouds,
The number of particles per unit volume,
TO FIND the minimum mass that a cloud with these properties needs in order to form a star
ASSUMPTION: The molecular cloud is assumed to be entirely made up of Hydrogen.
APPROACH:
The minimum mass of stability is
often called as Jean's mass . It is a
critical mass for the star formation, if
the cloud
collapses under its own gravity and if
there is
not sufficient gravity to support the pressure and the cloud may
fragment.
This Jean mass is given as
here is
the boltzmann constant,
is the
universal gravitational constant
is
the mass of the hydrogen atom
is the
temperature of the molecular cloud
is
the number of hydrogen atoms per unit volume.
Substituting the corresponding values of the constant we get,
This is the minimum mass of the cloud that could form a star.
The mass of the sun is ,
Therefore, the mass of the cloud