A metal rod, fixed at both ends, has a length l,area of cross section A and youngs modulus Y and coefficient of linear expansion α is heated through t0 C. The work done in heating the rod is
The work done is nothing but the potential energy stored.
Also, the thermal stress is given by TA=Yαt. We have,
W=12 (stress) (strain) (volume)
W=12×Yl×x2l×(Al) ..... (1)
Since x=TlYA and T=YAαt, we have on substituting in (1),
W=12YAlα2t2