Solve the following problem:
Consider a wire that undergoes an infinitesimal change from an initial equilibrium state to a final equilibrium state.
(a) Show that the change of tension is equal to
dζ = αAYdT + (AY/L)dL .
(b) A nickel wire of cross-sectional area 0.0085 em? under a tension of 20 N and a temperature of 20°C is stretched between two rigid supports 1 m apart. If the temperature is reduced to 8°C, what is the final tension?
(Note: Assume that Q and Y remain constant at the values of 1.33 x 10-5 K-1 and 2.1 x 106 Pa, respectively.)