A metal rod is 40.125 cm long at 20 °C and 40.148 cm long at 35 °C. calculate the coefficient of linear expansion of the rod for this temperature range.
change in length/length = k * change in T
k = (40.148-40.125)/(35-20) / 40.125
a = (L'-L)/(L*deltaT)
= (0.023/40.125)[1/(35-20)]
= 3.82*10^-5 (degC)^-1
To calculate the coefficient of linear expansion for the given temperature range, we can use the formula:
ΔL = α * L * ΔT
where:
ΔL = change in length
α = coefficient of linear expansion
L = initial length
ΔT = change in temperature
Given:
L_1 = 40.125 cm (initial length)
L_2 = 40.148 cm (final length)
T_1 = 20 °C (initial temperature)
T_2 = 35 °C (final temperature)
First, let's calculate the change in length (ΔL):
ΔL = L_2 - L_1
ΔL = 40.148 cm - 40.125 cm
ΔL = 0.023 cm
Next, let's calculate the change in temperature (ΔT):
ΔT = T_2 - T_1
ΔT = 35 °C - 20 °C
ΔT = 15 °C
Now, we can substitute the known values into the formula to find the coefficient of linear expansion (α):
ΔL = α * L * ΔT
0.023 cm = α * 40.125 cm * 15 °C
To solve for α, divide both sides of the equation by (40.125 cm * 15 °C):
α = (0.023 cm) / (40.125 cm * 15 °C)
Calculating α:
α ≈ 9.4912 x 10^(-6) / °C
Therefore, the coefficient of linear expansion for this temperature range is approximately 9.4912 x 10^(-6) / °C.
To calculate the coefficient of linear expansion of the metal rod, we can use the formula:
ΔL = α * L0 * ΔT
where:
- ΔL is the change in length of the rod,
- α is the coefficient of linear expansion,
- L0 is the original length of the rod, and
- ΔT is the change in temperature.
First, we need to find the change in length of the rod:
ΔL = L_final - L_initial
= 40.148 cm - 40.125 cm
= 0.023 cm
Next, we need to calculate the change in temperature:
ΔT = T_final - T_initial
= 35 °C - 20 °C
= 15 °C
Now, we plug these values into the formula to find the coefficient of linear expansion:
0.023 cm = α * (40.125 cm) * 15 °C
To find α, rearrange the formula:
α = ΔL / (L0 * ΔT)
= (0.023 cm) / [(40.125 cm) * (15 °C)]
Now, calculate the coefficient of linear expansion by substituting the values:
α ≈ 0.034 x 10^-3 cm/°C
Therefore, the coefficient of linear expansion for this temperature range is approximately 0.034 x 10^-3 cm/°C.