Question

Two thin strips of metal are bolted together at one end and have the same temperature. One is steel, and the other is aluminum. The steel strip is 0.11% longer than the aluminum strip. By how much should the temperature of the strips be increased, so that the strips have the same length?

Answer 1

Let the length of an aluminum strip be L and the length of a steel strip be 1.0011L, respectively.

We know that, L = L₀ (1 + T)

By how much should the temperature of the strips be increased, so that the strips have the same length?

L_steel =L_aluminium

L₀ (1 + _sT) = L₀ (1 + _AlT)

where, _s = thermal expansion coefficient of steel = 13 x 10^-60C^-1

_Al = thermal expansion coefficient of aluminium = 24 x 10^-60C^-1

then, we get

(1.0011 L) [1 + (13 x 10^-60C^-1) T] = L [1 + (24 x 10^-60C^-1) T]

(1.0011) + (13.0143 x 10^-60C^-1) T = 1 + (24 x 10^-60C^-1) T

(0.0011) = (10.9857 x 10^-60C^-1) T

T = (0.0011) / (10.9857 x 10^-60C^-1)

T = 100.1 ⁰C