Question

A brick is initially 14.98 cm high and an aluminum can is initially 14.99 cm high. By how much must their temperatures be raised in order for the brick and the can to have exactly the same height?

(I know its not found by doing

ΔL(Al)/L(Al) - ΔL(Br)/L(Br) = [α(Al) - α(Br)].ΔT

ΔL(Al) - ΔL(Br) = -0.01 = 15 x [(23 - 5.5) x 10^-6] x ΔT

which gives ΔT = - 38.09°C)

Answer 1

We know that,

L = Lo ( 1 + alpha delta T)

alpha(brick) = 5.5 x 10^-6 per deg C

alpha(aluminium) = 22.2 x 10^-6 per deg C

As per the given condition

Lo ( 1 + alpha(brick) delta T ) = Lo (1 + alpha(aluminium) delta T)

14.98 (1 + 5.5 x 10^-6 x delta T) = 14.99 (1 + 22.2 x 10^-6 x delta T)

1 + 5.5 x 10^-6 x delta T = 1.00067 + 22.2149 x 10^-6 delta T

16.7149 x 10^-6 delta T = -0.00067

delta T = -0.00067 / 16.7149 x 10^-6 = -40.084 deg

Hence, delta T​ = -40.084 deg C