Physics

Physics · modern-physics

Problem

i. During much of the collapse, the gas is so transparent that any heat generated is immediately radiated away, i.e. the ball stays in thermodynamic equilibrium with its surroundings. What is the number of times,

n

, by which the pressure increases when the radius is halved to

r_{1}=0.5 r_{0}

? Assume that the gas density remains uniform. Given constants: Problem T3. Protostar formation Let us model the formation of a star as follows. A spherical cloud of sparse interstellar gas, initially at rest, starts to collapse due to its own gravity. The initial radius of the ball is

r_{0}

and the mass is

m

. The temperature of the surroundings (much sparser than the gas) and the initial temperature of the gas is uniformly

T_{0}

. The gas may be assumed to be ideal. The average molar mass of the gas is

\mu

and its adiabatic index is

\gamma>\frac{4}{3}

. Assume that

G \frac{m \mu}{r_{0}} \gg R T_{0}

, where

R

is the gas constant and

G

is the gravitational constant.

Browse the problem library