We would like to increase the length of a 15 cm long copper rod of cross section `4mm^2` by 1 mm. The energy absorbedd by the rod if it is heated is `E_1`. The energy absorbed by the rod if it is stretched slowly is `E_2`. Then find `E_1//E_2`. [Variaous parameters of copper are density `=9xx10^3 Kg//m^(3)`, thermal coefficient of linear expansion `=16xx10^-6//K`, Young's modulus `=135xx190Pa`, specific heat `= 400 J//kg-K`]

Explanation

If temperature is inreased by `Deltatheta` then
`Deltal=lalphaDeltatheta`
`impliesDeltatheta=(Deltal)/(lalpha)`
`E_1=(rhoAl)SDeltatheta=rhoAlS(Deltal)/(lalpha)`
When stretched, stress`=Y(Deltal)/(l)`
`E_2=(1)/(2)(Y(Deltal)/(l))((Deltal)/(l))xxAl=(Y(Deltal)^2A)/(2l)`
So, `(E_1)/(E_2)=(2rhoSl)/(alpha(Deltal)Y)=500`