According to Stefan's law of radiation, a black body radiates energy `sigmaT^(4)` from its unit surface area every second where T is the surface temperature of the black body and `sigma=5.67xx10^(-8)W//m^(2)K^(4)` is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When detonated, it reaches temperature of `10^(6)` K and can be treated as a black body.
If all this energy U is in the form of radiation, corresponding momentum is `p=U/c`. How much momentum per unit time does it impart on unit area at a distance of 1 km ?

Explanation

Momentum in unit time,
`p=(U)/(c)`
`=(1.8xx10^(17))/(3xx10^(8))`
`=6xx10^(8)" N/s"`
Momentum in unit time per unit area is pressure,
`:.P=(p)/(A)`
`=(6xx10^(8))/(4pid^(2))`
`=(6xx10^(8))/(4xx3.14xx(10^(3))^(2))`
`=0.4777xx10^(2)`
`:.P=47.77" Nm"^(-2)`