L = Lo * k*Lo (T - To).
L = 20 + 1.7*10^-5*20(40 - 10),
L = 20 * 0.01020 = 20.01020cm.
L = 20 + 1.7*10^-5*20(40 - 10),
L = 20 * 0.01020 = 20.01020cm.
ΔL = L * α * ΔT
Where:
ΔL = Change in length
L = Initial length
α = Coefficient of linear expansion of copper
ΔT = Change in temperature
To find the new length, we need to calculate the change in length (ΔL) and then add it to the initial length (L).
First, let's calculate the change in length (ΔL):
ΔL = L * α * ΔT
Given:
L = 20 cm (Initial length)
α = Coefficient of linear expansion of copper (which is usually around 0.0000163 per degree Celsius for copper)
ΔT = 40 degrees Celsius - 10 degrees Celsius = 30 degrees Celsius (Change in temperature)
Plugging these values into the formula:
ΔL = 20 cm * 0.0000163 per degree Celsius * 30 degrees Celsius
ΔL ≈ 0.00978 cm (rounded to five decimal places)
Now, we can find the new length by adding the change in length to the initial length:
New Length = Initial Length + Change in Length
New Length = 20 cm + 0.00978 cm
New Length ≈ 20.00978 cm (rounded to five decimal places)
Therefore, the new length of the copper bar, when heated to a temperature of 40 degrees Celsius, will be approximately 20.00978 cm.