Question

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/2

This 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 1

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 area  be 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.