Adiabatic Process of uranium fission bomb

[Creebe]

Homework Statement

The fireball of a uranium fission bomb consists of a sphere of radius = 15m and temperature 300,000K shortly after detonation. Assuming that the expansion is adiabatic and that the fireball remains spherical, estimate the radius of the ball when the temperature is 3000K. (Take γ = 1.4)

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

Homework Equations

What equations do you need here?

The Attempt at a Solution

When you figure out the relevant equations, this becomes quite simple.

 

[Creebe]

okay i did

[math]TV\exp{γ-1} = constant
T = \frac{constant}{V\exp{γ-1}}
dT = (1-γ)V\exp{-γ)dV
[/math]

 

[rock.freak667]

okay i did

[math]TV\exp{γ-1} = constant
T = \frac{constant}{V\exp{γ-1}}
dT = (1-γ)V\exp{-γ)dV
[/math]

ok right if you have TV^γ-1= constant; then this means T₁V₁^γ-1=T₂V₂^γ-1. Right?

You can find V₁ since you are given the radius and you know T₁ and T₂, so all you need to get really is V₂

 

[Creebe]

oohh that's what the constant means. Okay! thanks!