Question

Steel bars each of length 3m at 28°C are to be used for constructing a rail line. If the linear expansivity of steel is 1.0 x 10^-5K^-1, what is the safety gap that must be left between successive bars, if the highest temperature expected is 40°C?​

Answer 1

The formula for calculating the length change due to a temperature change is:

ΔL = α * L * ΔT

where α is the linear expansivity, L is the original length of the bar, and ΔT is the change in temperature.

So in this case, the length change of each bar would be:

ΔL = 1.0 x 10^-5 K^-1 * 3m * (40°C - 28°C)

Converting the temperatures to Kelvin (28°C = 28 + 273 = 301 K and 40°C = 40 + 273 = 313 K), we get:

ΔL = 1.0 x 10^-5 K^-1 * 3m * (313 K - 301 K)

ΔL = 1.0 x 10^-5 * 3 * 12

ΔL = 0.00036 m

So each bar will increase in length by approximately 0.00036 meters when the temperature changes from 28°C to 40°C. To allow for this increase in length, a safety gap of 0.00036 meters should be left between each bar.