Question

At 17°C, a rod is exactly 18.08 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 250°C, where the rod now measures 18.25 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made? The linear expansion coefficient of steel is 11 x 10-6 1/C°.

Answer 1

Answer -

Given,

Initial Temperature = 17 C

Initial Length of rod = 18.08 cm

Final Temperature = 250 C

Final Length of rod = 18.25 cm

Linear expansion coefficient of steel = 11 * 10-6 / C

Thermal expansion for rod = ?

We know that,

L = LT

where,

L = change in length

L = Original Length

T = change in Temperature

= Linear coefficient of thermal expansion

Now,

The steel ruler and rod both are placed in the oven. So, both gets expanded.

The rod is measured by steel ruler. So, measurement of steel ruler is same as rod.

So,

For steel,

Ls = sLT

Ls = 11 * 10-6 / C * 18.25cm * (250 C - 17 C)

Ls = 0.04677475 cm

Now,

Expansion for rod = Lr + Ls

And,

Lr = Final Length of Rod - Initial Length of Rod

Lr = 18.25 cm - 18.08 cm

Lr = 0.17 cm

So,

Expansion for rod = 0.17 cm + 0.04677475 cm

Expansion for rod = 0.2168 cm

Now,

Lr = rLT

Put the values,

0.2168 cm = r * 18.25 cm * (250 C - 17 C)

0.2168 cm = r * 4252.25 Ccm

r = 0.2168 cm / 4252.25 Ccm

r = 5.1 * 10-5 /C [ANSWER]