1) A copper collar is to fit tightly about a steel shaft whose diameter is 6.009

Question

1) A copper collar is to fit tightly about a steel shaft whose diameter is 6.0095 cm at 23°C. The inside diameter of the copper collar at that temperature is 5.9800 cm. To what temperature must the copper collar be raised so that it will just slip on the steel shaft, assuming the temperature of both the steel shaft and copper collar are raised simultaneously?

2) A container is filled to the brim with 1.5 L of mercury at 20°C. As the temperature of the container and mercury is increased to 56°C, a total of 7.8 mL of mercury spill over the brim of the container. Determine the linear expansion coefficient of the material that makes up the container.

Explanation / Answer

linear expansion coeffiecient of copper = 16.6 x 10^-6 m / m K

of steel = 12 x 10^-6 m/m K

length change,

L = Lo (1 + alpha * deltaT)

Final diameter will be same for both.

Lo1 (1 + alpha1 deltaT) = Lo2 (1 + alpha2 deltaT)

5.9800 (1 + (16.6 x 10^-6 ( T - 23))) = 6.0095(1 + (12 x 106-6( T-23)))

(4.6 x 10^-6)T - 1.058 x 10^-4 = 0.0295

T = 6436 deg C

2. Linear expansion coeff of mercury = 61 x 10^-6 m / m K

increase in volume of mercury - increase in volume of container = 7.8 m L

deltaV = 3 * V * alpha * deltaT

3(1.5) (61 x 10^-6) (56 - 20) - 3(1.5) (alpha) (56 - 20) = 7.8 x 10^-3 Litre

9.882 x 10^-3 - 162 alpha = 7.8 x 10^-3

alpha = 12.85 x 10^-6 m / m K

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