An iron vat is 14 m long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure?

Answer 1

Since you did not specify which type of iron, I am using the expansion coefficient for forged iron, α=11,3 X10^-6 m/(m^oC); if this value does not agree with your text, you can change the value to the appropriate one.

The equation for the change in length is ΔL = α L_o ΔT, where L_o is the original length, ΔL = L - L_o , L is the new length and ΔT = T - T_o, where T_o is the original temperature and T is the new temperature.

This equation can be rewritten as: L = L_o [1 + α ( T - T_o )]

In this case, L_o = 14m, T = 100 ^oC, T_o = 20 ^oC,

L = (14m)[1 + (1.3 X10^-6 m/(m^oC))(100 ^oC - 20 ^oC)] = 14.001456m