Suppose that a brass rod 2.0 m long expands 0.2 cm when its temperature is increased a certain amount. By how much will a brass rod 80 m long expand with the same change in temperature?

0.08 m

Explanation:

Linear expansivity brass = 2 * 10^-5 C

Linear expansivity = change in length / (initial length * θ)

Change in length = 0.2cm = 0.002m

Initial length = 2m

2 * 10^-5 = 0.002 / (2 * θ)

(2 * 10^-5 * 2θ) = 0.002

4 * 10^-5θ = 0.002

θ = 0.002 / 4 * 10^-5

θ = 2 * 10^-3 / 4 * 10^-5

θ = 0.5 * 10^2

θ = 50°C

For a rod of original length 80m at the same temperature of 50°C

Linear expansivity = change in length / (initial length * θ)

Change in length = dL

2 * 10^-5 = dL / (80 * 50)

2 * 10^-5 * 80 * 50 = dL

160 * 10^-5 * 50 = dL

8000 * 10^-5 = dL

0.08 m = dL

Hence, change in length = 0.08m

ingenuity says that the answer is 2.7 m.