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Two metallic spheres S1 and S2 are made up of the same material and have got identical surface finish.The mass of S1 is thrice that of S2.Both the spheres are heated to same temperature and placed in the same room having lower temperature but are thermally insulated from each other.Find the the ratio of the initial rate of cooling of S1 to that of S2?
rate of thermal radiation is directly proportional to ((Tsphere)^4-(Texternal)^4)=dQ/dt
rate of cooling=d(Tsphere)/dt=-mass*specific heat capacity*dQ/dt
SINCE THE MATERIAL IS SAME THEN THEIR MOLAR HEAT CAPACITY WOULD BE SAME
LET M1 BE THE MASS OF S1 AND M2 BE THE MASS OF M2 ...THEN M1=3M2.................(1)
NOW HEAT FOR S1 (dQ)=M1*S*dT.................. WHERE (S IS MOLAR HEAT CAPACITY , dT IS CHANGE IN TEMPRATURE)
THEREFORE (dQ/dt)=M1*S*(-dT/dt)................(2) where ( dt IS CHANGE IN TIME THE MINUS SIGN INDICATES THAT THE CAS IS COOLING)
SIMILARLY FOR S2 (dQ/dt)=M2*S*(-dT/dt)..........................(3)
from EQUATION (1),(2),(3) WE GET THE RATIO AS M1/M2 WHICH IS 3/1...........................ANSWER
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