How much longer is it when it contains boiling water at 1 atm pressure?

Question

An aluminum vat is 12 m long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure?

Answer 1

Fractional Thernal expansion coefficient for Al: 24x10^-6 per ^oC (at 20 ^oC)

Water boils at 100^oC at 1 atm pressure.

Assuming this fractional expansion remains constant over the whole temperature change:

ΔL / L_o = ∝ ΔT

ΔL = ∝ ΔT L_o = 24x10^-6 / ^oC • (100^oC-20^oC) • 12m = 0.023m (23 mm, about 9/10^ths of an inch)