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)

Question

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)

Answer 1

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.

Answer 2

To calculate the difference in lengths between the iron and the brass, we can use the formula for linear expansion:

ΔL = L₀ * α * ΔT

Where:
ΔL is the change in length
L₀ is the initial length
α is the linear expansivity
ΔT is the change in temperature

1. Calculate the change in temperature for both the iron and the brass:
ΔT_brass = (820 - 20) = 800°C
ΔT_iron = (770 - 20) = 750°C

2. Calculate the change in length for both the iron and the brass:
ΔL_brass = (10 * 0.000019 * 800) = 0.152 cm
ΔL_iron = (10 * 0.000012 * 750) = 0.09 cm

3. Calculate the difference in lengths:
Difference in lengths = ΔL_brass - ΔL_iron
Difference in lengths = 0.152 cm - 0.09 cm
Difference in lengths = 0.062 cm

Therefore, the difference in lengths between the iron and the brass is 0.062 cm.