# 物理熱力學問題...尋求高人指點

A heavy brass bar has projections at its ends. Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20 c. What is the tensile stress in the steel wires when the temperature of the system is raised to 150 c? Make any simplifying assumptions you think are justified.

Rating

Let L be the length of he brass bar at 20'C

Expansion of the brass bar when its temperature is raised to 150'C

= L.a(brass).(150-20) = 130L.a(brass)

where a(brass) is the coefficient of linear expansion of brass

Similarly, expansion of the steel wire when its temperature is raised to 150'C

= L.a(steel).(150-20) = 130L.a(steel)

where a(steel) is the coefficient of linear expansion of steel

The difference in length = 130.L[a(brass)-a(steel)]

From the web, it can be found the the values of coefficient of expansion are:

a(brass) = 19x10^-6 /C and a(steel) = 12x10^-2 /C

Hence, difference in length = 130x7x10^-6.L = (9.1x10^-4)L

Since Young's modulus E = stress/strain

but strain = 9.1x10^-4L/L = 9.1x10^-4

Thus, stress = (9.1x10^-4)E

where E is the Young's Modulus of steel (try to look up its value from your physics textbook or from the web and use it to calculate the stress).