To calculate the difference in lengths of the iron and brass, we need to use the formula for linear expansion:
ΔL = α * L * ΔT
where:
ΔL is the change in length
α is the linear expansivity
L is the original length
ΔT is the change in temperature
Given:
Length of the compound strip (L) = 10cm
Temperature of brass (T₁) = 20°C
Temperature of iron (T₂) = 770°C
Linear expansivity of brass (α₁) = 0.000019K
Linear expansivity of iron (α₂) = 0.000012K
First, we need to calculate the change in temperature for both the brass and iron using the formula:
ΔT = T₂ - T₁
ΔT(brass) = 820°C - 20°C = 800°C
ΔT(iron) = 770°C - 20°C = 750°C
Next, we can calculate the change in length for both the brass and iron:
ΔL(brass) = α₁ * L * ΔT(brass)
ΔL(iron) = α₂ * L * ΔT(iron)
ΔL(brass) = 0.000019 * 10cm * 800°C = 0.152cm
ΔL(iron) = 0.000012 * 10cm * 750°C = 0.09cm
Finally, we can find the difference in lengths between the iron and brass:
Difference in lengths = ΔL(brass) - ΔL(iron)
Difference in lengths = 0.152cm - 0.09cm = 0.062cm
Therefore, the difference in lengths between the iron and brass is 0.062cm.
A compound strip of the brass and iron is 10cm long at 20 °C is held horizontally with the iron uppermost when heated from below with the Bunsen burner. The temperature of the brass is 820°C and of the iron is 770°C. Calculate the difference in lengths of the iron and the brass. (Given linear expansivity of brass=0.000019K and of the iron is 0.000012K)
1 answer