# Ball of gas experiences rapid increase in pressure...

## Homework Statement

A self-gravitating ball of gas suddenly experiences a rapid increase in its pressure to a new value P'. Taking average density of the star to be ρ and radius R, and ignoring gravity altogether, estimate the time scale of expansion of the star.

## Homework Equations

Force= Pressure/Surface area= mass x Acceleration

## The Attempt at a Solution

Considering an outer shell of thickness δr and radius r:
Outward force on shell = (P(r) - P(r + δr)) 4πr2
My question is really why is the P(r + δr) the minus of it?

I'm comfortable doing the rest of the question by just using equation mass of shell x acceleration and equating them and using dimensional analysis on that .
But I'm unsure why it's a minus there, i'm fairly certain that's right after speaking classmates but I don't understand why.

Thanks in advance.

## Answers and Replies

BvU
Science Advisor
Homework Helper
My question is really why is the P(r + δr) the minus of it?
Because it works inwards ! Make a little sketch for a thin shell at r .