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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

dT = -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.)

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