A copper bar is initially 20 cm long at 10 degrees C. It is then heated to a temperature of 40 degrees C. What will be its new length?

L = Lo * k*Lo (T - To).

L = 20 + 1.7*10^-5*20(40 - 10),
L = 20 * 0.01020 = 20.01020cm.

CORRECTION: L=20 + 0.01020=20.01020cm.

To determine the new length of the copper bar, we can use the principle of thermal expansion. Copper expands when heated and contracts when cooled. The formula to calculate the change in length due to temperature change is given by:

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.