The luminosity density of an accretion disk, which extends from riso to rmax, is given by the blackbody Planck's formula Ιναν Tmax 12 Sam r ehv/kBT(r) BT(r) – 1 dr, rlso where is the radiation frequency, T (r) is the temperature in the disc at radius r, h is the Planck's constant and kB is the Boltzmann's constant. Show that, in the limit hv <1, L, is proportional to 12. KBT

Longs Van aw rejtoug] - consider a liquid mixture of components 1,2, 3, 4. The excess Gibbo energies of all the binaries, formed by these components obey relations of the formi Aijxjxj G₁₁ RT where Alj is the const characteristic of the i-j binary. Desire an expression for the co-efficient of component-I in the quaternary solution. وعاد سامانه . NL = enemical Engg Thermodyamies Question Torture TA gif croftrum svedo sit

Problem 2: Black hole – the ultimate blackbody A black hole emits blackbody radiation called Hawking radiation. A black hole with mass M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of hc³/167²KGM. a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole. b) Calculate the total power radiated by a one-solar mass black hole. c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing. As it loses energy, its mass must decrease; one could say "evaporates". Derive a differential equation for the mass as a function of time, and solve to obtain an expression for the lifetime of a black hole in terms of its mass.

A cloud of mean number density n ~ 3000 cm-3 and radius 3 pc has an ionising source with luminosity at 13.6 eV of L13.6eV = 2.18 x 109 erg s- at the centre. (a) What is the size of the HII region in pe? [og = 2 x 10-13 cms-]. %3D (b) What assumptions are involved in part a) (c) Discuss why the HII region will drive a shock into the rest of the cloud, and calculate the post-shock density. (d) Show why this HII region will destroy the cloud.