Question

Suppose that at room temperature, a certain aluminum bar is 1.0000 m long. The bar gets longer when its temperature is raised. The length l of the bar obeys the following relation: l=1.0000+2.4×10−5T, where T is the number of degrees Celsius above room temperature. What is the change of the bar's length if the temperature is raised to 13.6∘C above room temperature?

Answer 1

When T = room temperature L = 1.0000m+2.4×10^-5m/°C*0°C = 1.0000m+0=1.0000m change in the length = l2-l1 = (1.0000m+2.4×10^-5m/°C*T2)-(1.0000m+2.4×10^-5m/°C*T1) = 1.0000m+2.4×10^-5m/°CT2-1.0000m-2.4×10^-5m/°CT1=2.4×10^-5m/°CT2-2.4×10^-5m/°CT1=2.4×10^-5m/°C(T2-T1) So we don’t need at all the 1.0000m data, we just need T2-T1, which is the difference between room temperature and the current temperature, which is 13.6°C. change in the length = 2.4×10^-5m/°C*13.6°C = 3.264*10^-4m = 0.3264 mm = 326.4 micrometers