In: Physics
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 -
Given,
Initial Length of rod = 18.08 cm
Final Length of rod = 18.25 cm
Linear expansion coefficient of steel = 11 * 10-6 / C
Thermal expansion for rod = ?
We know that,
where,
= 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 = 11 * 10-6 / C * 18.25cm * (250 C - 17 C)
Now,
And,
Lr = Final Length of Rod - Initial Length of Rod
So,
Expansion for rod = 0.17 cm + 0.04677475 cm
Expansion for rod = 0.2168 cm
Now,
Put the values,
0.2168 cm = r * 18.25 cm * (250 C - 17 C)