According to Stefan’s law of radiation, a black body radiates energy from its unit surface area every second where T is the surface temperature of the black body and is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When denoted, it reaches temperature of 106K and can be treated as a black body.
a) estimate the power it radiates
b) if surrounding has water at , how much water can 10% of the energy produced evaporate in 1 sec?
c) if all this energy U is in the form of radiation, corresponding momentum is . How much momentum per unit time does it impart on unit area at a distance of 1 km?
Given: E = per sec per sq. m
Thus, total E is equal to radiated from all surface area A per second will be power radiated by nuclear weapon
Thus, P =
Now, &
…. (R = 0.5m, T = 106K)
Thus,
…… (i)
(b) from (i)
Now, for evaporation of water 10% of this power is required.
Thus,
Now, energy required by m kg of water at to evaporate at = E required to heat up water from + E required to evaporate water into vapour
Thus,
(c) Now, we know that,
Momentum per unit time
Thus,
Required momentum per unit time