The coefficient of volume expansion for iron is 3.6 x 10-5/Co. If a 17 m long rod of iron is cooled from 100oC to 5oC, what it the new length?
The temperature decreases by 95 C, so the length decreases by
L*(1.2*10^-5)*95 = 1.94*10^-2 m
= 1.94 cm
Note that I had to use 1/3 of the coefficient of volume expansion for the coefficient of linear expansion. That is becasue the iron expands in all three dimensions.
α=ΔL/L•ΔT
ΔL = α• L•ΔT=3.6•10⁻⁵•17• (5-100) =
= -0.05814 m
α=ΔL/L•ΔT
α=3.6•10⁻⁵/3
ΔL = 3.6•10⁻⁵•17• (5-100)/3 =
= -0.05814/3=0.01938 m
To find the new length of the iron rod after it is cooled from 100°C to 5°C, we need to use the coefficient of volume expansion for iron.
The coefficient of volume expansion for a material represents how much the volume of that material increases or decreases with a change in temperature. It is denoted by the symbol β (beta) and has units of per degree Celsius (°C).
In this case, the coefficient of volume expansion for iron is given as 3.6 x 10^(-5) / °C.
The formula to calculate the change in length (ΔL) due to a change in temperature (ΔT) for a material is given by:
ΔL = L0 * β * ΔT
Where:
- ΔL is the change in length
- L0 is the original length of the material
- β is the coefficient of volume expansion
- ΔT is the change in temperature
Given:
- Initial length (L0) = 17 m
- Initial temperature (T0) = 100°C
- Final temperature (T1) = 5°C
Now we can substitute these values into the formula and solve for ΔL to find the change in length:
ΔL = 17 m * (3.6 x 10^(-5) / °C) * (5°C - 100°C)
ΔL = 17 m * (3.6 x 10^(-5) / °C) * (-95°C)
Note: We need to use the change in temperature (T1 - T0) which is -95°C since the rod is being cooled.
Calculating the value:
ΔL = 17 m * (3.6 x 10^(-5)) * (-95)
ΔL ≈ -0.05814 m
The negative sign indicates that the rod has contracted in length due to cooling.
To find the new length, we can subtract the change in length from the initial length:
New Length = L0 + ΔL
New Length = 17 m - 0.05814 m
New Length ≈ 16.94186 m
Therefore, the new length of the iron rod is approximately 16.94186 meters after it is cooled from 100°C to 5°C.