A Brass rod 50.0 cm long expands 0.0734 cm when heated. Find the temperature change.
To find the temperature change, we can use the formula for linear expansion:
ΔL = α * L₀ * ΔT
where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L₀ is the original length, and
ΔT is the change in temperature.
In this case, we know that:
ΔL = 0.0734 cm,
L₀ = 50.0 cm,
and we need to solve for ΔT.
Rearranging the formula, we get:
ΔT = ΔL / (α * L₀)
To find α, which is the coefficient of linear expansion for brass, you can look it up in a reference book or online database. The coefficient of linear expansion for brass is approximately 0.000019 (1/°C).
Substituting the known values into the formula, we have:
ΔT = 0.0734 cm / (0.000019 (1/°C) * 50.0 cm)
Calculate the answer using a calculator:
ΔT = 76.8421 °C
Therefore, the temperature change is approximately 76.8421 °C.