Show that, for an elastic rod of length L per unit mass at temperature T and under a tensile…

Show that, for an elastic rod of length L per unit mass at temperature T and under a tensile force F.

where cL denotes the specific heat at constant length.

The equation of state for a particular rod is

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where k is a constant and L0 , the length at zero tension, depends on temperature only. Show

(a) that the work which must be done on the rod to stretch it isothermally and reversibly from the length Ln to 2L is kTL0 and

(b) that the change in internal energy of the rod is

where  is the coefficient of expansion at zero tension, i.e.

 

 

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