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ll O1 Slale of the substance and ue atio, ajb. 2-26 From the equation of state given in Eq. (2-12) compute (a) the rate at which the length of a rod changes with temperature when the tension is kept constant; (b) the rate at which the length changes with tension when the temperature is constant; (c) the change dT in temperature that is necessary to keep the length constant when there is a small change ds in the tension. Assume Youngs modulus is independent of temperature. 2-27 A railrnad trnol i

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Answer #1

The equation of state is L=4,11+_+α(TZ) YA The rate of change of length of the rod changes with temperature at a constant tension F can be obtained by partially differentiating the above equation with respectto temperature. Since the tension is constant, the F is used as a subscript for the derivative a(T-T O1 a (LF OL ат OL OT OL The rate of change of length with tension at constant temperature is obtained by partially differentiating the length at constant temperature o (T-T) OF OL L OF YA OL The change in dT that is necessary to keep the length fixed when the tension changes by dF is obtained by taking a total derivative of the equation of state and setting dT to zero YA YA

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