Question

In a certain bimetallic strip, the brass strip is 0.100% longer than the steel strip at a temperature of 295°C. At what temperature do the two strips have the same length? Coefficients of linear expansion for steel α = 12.0 × 10−6 K−1 and for brass α = 19.0 × 10−6 K−1

Answer 1

Lsi = 1000 meters
Lbi = 1001 meters

delta Ls = 1000 * 12.0 * 10^-6 * dT
delta Lb = 1001 * 19.0 * 10^-6 * dT
but
delta Ls = 1 + delta Lb
delta Ls = 1000 * 12.0 * 10^-6 * dT = 1 + 1001 * 19.0 * 10^-6 * dT
dT is going to be negative of course

Answer 2

1000 * 12.0 * dT = 10^6 + 1001 * 19.0 * dT
(12000 - 19019) dT = 10^6
- 7019 dT = 1,000,000
dT = - 142
so 295 - 142 = 153 deg