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 ?

According to Stefan's law of radiation, a black body radiates energy s

1.	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 ?
Answer» Solution :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)`