A brass rod is heated from 295 K to 400 K. At 295 K the rod is 2,5 m long. The linear expansion coefficient of brass is 20 × 10-6/K. Calculate the final length of the rod.
The formula for linear expansion is:
ΔL = α * L * ΔT
where:
ΔL = change in length
α = linear expansion coefficient
L = initial length
ΔT = change in temperature
Given:
α = 20 × 10^-6/K
L = 2.5 m
ΔT = 400 K - 295 K = 105 K
Plugging in the values:
ΔL = (20 × 10^-6/K) * 2.5 m * 105 K
ΔL = 0.000020 * 2.5 * 105
ΔL = 0.000020 * 262.5
ΔL = 0.00525 m
The final length of the rod will be:
Final length = Initial length + Change in length
Final length = 2.5 m + 0.00525 m
Final length = 2.50525 m
Therefore, the final length of the brass rod when heated from 295 K to 400 K is 2.50525 meters.