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What is the value of coefficient of area expansion for a sphere? Assume coefficient of linear expansion is α.(a) 2α(b) α(c) 3α(d) α/2This question was addressed to me in class test.Origin of the question is Thermal Expansion topic in chapter Thermal Properties of Matter of Physics – Class 11

Answer»

Right option is (a) 2α

For explanation: The AREA(A) of a SPHERE is 4πr^2.When the temperature INCREASES by ΔT, let CHANGE in areabe dA.Let the radius INCREASE by dr.The coefficient of area expansion is (dA/A)/ΔT.

∴ dA = 4π(r – dr)^2– 4πr^2 ≅ 8πrdr.

Also, dr = rαΔT.

The coefficient of area expansion is (dA/A)/ΔT

= (8πr*rαΔT/4π) / ΔT

= 2α.



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