If the diameter of a brass sphere is 2.540 cm at 31.00 degree C, what will its d

Question

If the diameter of a brass sphere is 2.540 cm at 31.00 degree C, what will its diameter be at a temperature of 107.5 degree C? The coefficient of linear expansion of brass is 19 Times 10^-6/ degree C. (Give your answer to at least three decimal places.) For the volume of the sphere to increase by 1.160%, to what temperature should the sphere be heated? The coefficient of volume expansion is 3 times that of linear expansion for the metal. What is the equation describing the volume expansion due to temperature changes?

Explanation / Answer

part B :

Formula for the Coefficient of Volume expansion

gamma g = change in volume /(initla Volume * change of temperature)

i,e g = dV/(V * dT)

dV/V = 1.16 % = 1.16/100 = 0.0116

also gamma g = 3 * Alpha = 3* 19 e -6

so

dT = change of temperature = (dV/v) *(1/g)

dT = 0.0116/(3*19 e -6)

dT = 203.508 deg C

dT = T2-T1 = 203.508

T2 = final tmeperature = 203.508 + 31 = 203.508 deg C

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