Two metallic spheres P and Q are of same surface finish and same density. Weight of P is twice that of Q. Both spheres are heated to same temperature and are left in room to cool by radiation. The ratio of initial rate of cooling of P to that of Q is

Question

Infinity Learn · Accepted Answer

Let the mass of Q be m.∴mass of P $$=$$ $$2mNow$$,  −m.s.$$dTdt=e$$σ.(4$$$$π$$$$R2)(T4$$−$$T04)⇒−$$dTdt=e$$σ.(4$$$$π$$$$R2)43$$$$π$$$$R3$$ρ$$S(T4$$−$$T04)⇒−$$dTdt=3e$$σρ$$S1R(T4$$−$$T04)$$∴−dTdt∝$$1RNow$$ $$43$$$$π$$$$Rp3$$ρ$$=2$$×$$43$$$$π$$$$RQ3$$ρ⇒$$Rp=(2)1/3$$.RQ∴Initial rate of cooling of PInitial rate of cooling of $$Q=RQRP=1(2)1/3$$

Two metallic spheres P and Q are of same surface finish and same density. Weight of P is twice that of Q. Both spheres are heated to same temperature and are left in room to cool by radiation. The ratio of initial rate of cooling of P to that of Q is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material