Serway & Jewett — Temperature: Problem 31

Two metal bars are made of invar and a third bar is made of aluminum. At $0^\circ\text{C}$, each of the three bars is drilled with two holes $40.0\text{ cm}$ apart. Pins are put through the holes to assemble the bars into an equilateral triangle as in Figure P18.31. (a) First ignore the expansion of the invar. Find the angle between the invar bars as a function of Celsius temperature. (b) Is your answer accurate for negative as well as positive temperatures? (c) Is it accurate for $0^\circ\text{C}$? (d) Solve the problem again, including the expansion of the invar. Aluminum melts at $660^\circ\text{C}$ and invar at $1427^\circ\text{C}$. Assume the tabulated expansion coefficients are constant. What are (e) the greatest and (f) the smallest attainable angles between the invar bars?