4) A cloud of molecular hydrogen is observed to have temperature of T = 10 K, and density ng = 100 cm . In the following

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4 A Cloud Of Molecular Hydrogen Is Observed To Have Temperature Of T 10 K And Density Ng 100 Cm In The Following 1 (42.43 KiB) Viewed 19 times

4) A cloud of molecular hydrogen is observed to have temperature of T = 10 K, and density ng = 100 cm . In the following, assume that the cloud is spherical, homogeneous and isotropic. (i) Prove that the potential energy of the cloud is 3 GM2 E, where M is the total mass of the cloud and r is its radius. (2/20) (i) Assume that the cloud is in hydrostatic equilibrium, and that no external pressure is acting on it. Using the virial theorem (which you don't need to prove), calculate the Jeans mass of the cloud. Note: You can use M = Num, where M is the mass of the cloud, m, is the proton's mass and you may assume = 2 for molecular hydrogen. You may express your result in terms of the solar mass, M = 2 x 10"gr. (6/20) (iii) Calculate the radius of the cloud that would fulfil the Jeans criterion. (2/20) (iv) Given that the cooling function of the cloud is A(T) = 10-23 erg - cm (independent on its temperature), calculate the cooling time toal of the cloud. (3/20)