A Brass rod 50.0 cm long expands 0.0734 cm when heated. Find the temperature change.
Linear Temperature Expansion Coefficient
α =ΔL/(L•ΔT),
for Brass α = 18.7•10^-6 K^-1,
ΔT = ΔL/(L• α) =
= 0.000734/(0.5•18.7•10^-6)=
= 78.5 K
To find the temperature change, we need to use the formula for thermal expansion:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length of the brass rod (0.0734 cm)
α is the coefficient of linear expansion for brass (inversely given from the length)
L0 is the original length of the brass rod (50.0 cm)
ΔT is the change in temperature we are trying to find
First, we need to find the coefficient of linear expansion for brass. The coefficient of linear expansion for brass is typically around 19 × 10^(-6) per degree Celsius.
So α = 19 × 10^(-6) / cm°C
Substituting the given values into the formula, we have:
0.0734 cm = (19 × 10^(-6) / cm°C) * (50.0 cm) * ΔT
Simplifying the equation gives:
ΔT = (0.0734 cm) / [(19 × 10^(-6) / cm°C) * (50.0 cm)]
Now, let's calculate ΔT:
ΔT = (0.0734 cm) / [(19 × 10^(-6) / cm°C) * (50.0 cm)]
= (0.0734 cm) / (0.00095 cm/°C)
≈ 77.16 °C
Therefore, the temperature change is approximately 77.16 °C.
To find the temperature change, we can use the linear expansion equation:
ΔL = α * L * ΔT
Where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L is the original length, and
ΔT is the change in temperature.
In this case, the change in length is given as 0.0734 cm, and the original length is 50.0 cm. We need to find the change in temperature (ΔT).
Rearranging the equation, we have:
ΔT = ΔL / (α * L)
Now, we need to find the coefficient of linear expansion for the brass rod. The coefficient of linear expansion varies depending on the material.
For brass, the average coefficient of linear expansion is approximately 0.000019 (1/°C).
Substituting the values into the equation:
ΔT = 0.0734 cm / (0.000019 (1/°C) * 50.0 cm)
Simplifying:
ΔT = 0.0734 cm / (0.000019 cm/°C * 50.0 cm)
ΔT = 0.0734 cm / 0.00095 cm/°C
ΔT ≈ 77.26 °C
Therefore, the temperature change is approximately 77.26 °C.