When the centre of earth is at a distance of $$1.5$$ x $$1011$$ m from the centre of sun, the intensity of solar radiation reaching at the earth's surface is $$1.26$$ $$kW/m2$$. There is a spherical cloud of cosmic dust, containing iron particles. The melting point for iron particles in the cloud is $$2000$$ K. Find the distance of iron particles from the centre of sun at which the iron particles start melting (in$$ x $$109$$ $$m). (Assume$$ sun and cloud as a black body,σ$$=5.6$$×$$10$$−$$8W/m2K4)

Question

Infinity Learn · Accepted Answer

$$d1$$ $$=$$ Distance between sun and $$cloudd2$$ $$=$$ distance between sun and earthPs $$=$$ Power of sun $$=1.26$$×$$103$$×$$4$$π×$$d22Let$$ the radius of particle is r so in equilibrium        Pemission $$=Pabsorption$$ ⇒ $$4$$σ$$T4=$$π$$r2$$×$$PS4$$$$π$$$$d12$$        $$4$$σ$$T4=14$$$$π$$$$d12$$×$$1.26$$×$$103$$×$$4$$$$π$$$$d22$$⇒    $$d1=d22T21.26$$×$$1035.6$$×$$10$$−$$8$$⇒     $$d1=1.5$$×$$10112$$×$$4$$×$$106$$×$$15$$×$$104$$⇒     $$d1$$≃$$2.81$$×$$109m$$

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App