An aluminum vat is 19 m long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure? m

Question

An aluminum vat is 19 m

 long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure?

 m

Answer 1

Step 1: Formula

ΔL = α L₀ΔT

where:

1. α = coefficient of linear expansion for aluminum =
2. L₀=19 m
3. ΔT = T_f - T_i

Step 2: Known Values

Boiling water at 1 atm → 100°C ΔT = T_f - T_i = 100 - 20 = 80 ⁰ C

α = 2.3 x 10^-5

Step 3: Calculate Expansion

ΔL = α L₀ΔT = 2.3 x 10^-5 x 19 x 80 = 0.03496 m =~ 0.035 m

Step 4: Convert to centimeters:

0.035m = 3.5cm