A steel bolt and a brass bolt are placed end-to-end, separated by a 0.1 cm gap. At what temperature will the bolts touch?

here are the solutions to the problems:

a) At what temperature will the bolts touch?

Note: The initial lengths of the steel and brass bolts are not provided in the problem statement. To solve this, we must assume that the problem intends for us to calculate the temperature change required for the sum of the expansions of the two bolts to equal the initial gap. However, without the individual initial lengths of the bolts, we cannot determine their individual expansions or the total expansion.

Assumption: Given the lack of specific lengths for the steel and brass bolts, a common interpretation for such problems is that the total length of the expanding system is not explicitly given, but the total expansion needed is the gap. If we assume the bolts are