Question

Sho w that the following relations hold for a reversible adiabatic 

expansion o f an idea l gas: 

The firebal l o f a uraniu m fissio n bom b consist s o f a spher e o f ga s 

of radiu s 15 m and temperatur e 300000 K shortl y after detonation . 

Assuming that the expansion is adiabatic and that the fireball remain s 

spherical, estimat e th e radiu s o f the bal l whe n th e temperatur e i s 

3000 K. (Tak e y=1.4.) 

Answer 1

2

these formula will be used

$\bigstar$

TV^γ-1 = constant .......(1)

$\bigstar$

T₁V₁^γ-1=T₂V₂ ^γ-1 ..........(2)

we can find V₁ as we have given radius , and also we know t₁ and t₂ , further we can find V₂

V₁ = volume of sphere

V=4/3πr³

(r= 15m)

On solving

We got

V₁ = 14137.17m³

and

T₁= 300000 K

T₂= 3000 K

γ-1 = 1.4 -1

= 0.4

now we solve for V₂

V₂ ^γ-1 = $T_1V_1^{γ-1} \over T_2$

On solving we got

V_{2 =} (1413710684.13)m³

And r= $({3V\over 4\pi }){^1\over3}$

r₂ = 438.54m