Question:

A metal rod of length 1.5 m and rectangular cross-section with dimensions 2 cm x 4 cm is initially at a uniform temperature of 20°C. The rod is then heated on one end by applying a flame which maintains a constant temperature of 500°C. The rod is allowed to reach thermal equilibrium.

(a) Calculate the change in length of the rod when it reaches thermal equilibrium. (b) Determine the coefficient of linear expansion for the metal used in the rod.

Given: Length of the rod, L = 1.5 m Initial temperature, T₁ = 20°C Temperature of the flame, T₂ = 500°C Width of the rod, w = 2 cm Height of the rod, h = 4 cm Coefficient of linear expansion, α = ?

Answer:

(a) To calculate the change in length of the rod, we need to use the formula:

ΔL = α * L * ΔT

Where: ΔL is the change in length α is the coefficient of linear expansion L is the original length of the rod ΔT is the change in temperature

To find ΔT, we subtract the initial temperature from the temperature of the flame:

ΔT = T₂ - T₁ = 500°C - 20°C = 480°C

Now, we can calculate the change in length:

ΔL = α * L * ΔT

Plugging in the given values:

ΔL = α * 1.5 m * 480°C

(b) To determine the coefficient of linear expansion, we rearrange the equation:

α = ΔL / (L * ΔT)

Plugging in the values:

α = ΔL / (1.5 m * 480°C)

Simplifying the equation:

α = ΔL / 720°C

Therefore, the coefficient of linear expansion for the metal used in the rod is ΔL / 720°C.

Note: The specific metal used in the rod might have a known coefficient of linear expansion, so the calculated value can be compared to known values to identify the metal used.