Question

A uniform metal rod of 2 mm² cross section is heated from 0°C to 20°C. The coefficient of linear expansion of the rod is 12 × 10^-6/°C, it's Young's modulus is 10¹¹ N/m². The energy stored per unit volume of the rod is ______.

Options

• 2880 J/m³

• 1500 J/m³

• 5760 J/m³

• 1440 J/m³

Answer 1

A uniform metal rod of 2 mm² cross section is heated from 0°C to 20°C. The coefficient of linear expansion of the rod is 12 × 10^-6/°C, it's Young's modulus is 10¹¹ N/m². The energy stored per unit volume of the rod is 2880 J/m³.

Explanation:

`"Energy"/"Volume" = 1/2 xx "stress" xx "strain"`

= `1/2 xx (YalphaDeltaT) xx ((Deltal)/l)`

= `1/2YalphaDeltaT xx ((lalphaDeltaT)/l)`

= `1/2Yalpha^2(DeltaT)^2 = 2880  J"/"m^3`