the coefficient of volume expansion for iron is 3.6 X 10^-5/C degrees. If a 17 m long rod of iron is cooled from 100 degrees C to 5 degrees C, What is the new length?
Coefficient of Linear Exp.=(3.6*10^-5)/3
= 1.2*10^-5/C.
L = Lo + a*(T-To)Lo
L = 17 + 1.2*10^-5*(5-100)17 =
17 - 0.0194 = 16.981 m.
To find the new length of the iron rod, we can use the formula for linear expansion:
ΔL = αLΔT
Where:
- ΔL is the change in length
- α is the coefficient of linear expansion
- L is the original length
- ΔT is the change in temperature
In this case, we are given:
- α = 3.6 × 10^(-5)/°C (coefficient of volume expansion for iron)
- L = 17 m (original length)
- ΔT = 100 °C - 5 °C = 95 °C (change in temperature)
Now let's calculate the new length by substituting these values into the formula:
ΔL = (3.6 × 10^(-5)/°C) * (17 m) * (95 °C)
ΔL = 6.174 × 10^(-2) m
The change in length is 6.174 × 10^(-2) meters. To find the new length, we need to subtract this change from the original length:
New Length = Original Length - Change in Length
= 17 m - 6.174 × 10^(-2) m
New Length ≈ 16.939 m
Therefore, the new length of the iron rod is approximately 16.939 meters.