The different in length between a brass and iron rod is 14cm at10°c . What must be the of the iron for this difference to remain at 14cm when both rods are heated to 10°c? Give that the linear expansivity of brass=19 and iron= 12

Answer 1

Let Lb be the original length of the brass rod and Li be the original length of the iron rod.

We know that the difference in length between the brass and iron rod at 10°C is 14cm. Therefore:

Lb - Li = 14

When both rods are heated to 10°C, their lengths will increase according to their linear expansivity. Let's denote the final lengths of the brass and iron rods as Lb' and Li' respectively.

The increase in length for the brass rod is given by:

ΔLb = Lb * αb * ΔT

ΔLb = Lb * 19 * 10

ΔLb = 190Lb

The increase in length for the iron rod is given by:

ΔLi = Li * αi * ΔT

ΔLi = Li * 12 * 10

ΔLi = 120Li

Since the difference in length remains at 14cm, we have:

Lb' - Li' = 14

(Lb + ΔLb) - (Li + ΔLi) = 14

Lb + 190Lb - (Li + 120Li) = 14

191Lb - 121Li = 14

Divide by 7:

191Lb/7 - 121Li/7 = 2

27.29Lb - 17.29Li = 2

Now we can substitute the value of Lb - Li from the first equation:

27.29(14+Li) - 17.29Li = 2

381.06 + 27.29Li - 17.29Li = 2

10Li = -379.06

Li = -37.9 cm

The length of the iron rod must be -37.9 cm for the difference in length to remain at 14cm when both rods are heated to 10°C. However, a negative length is physically unrealistic, so the situation described is not possible with the given linear expansivities.