Question

Expansion joints are used for materials that easily expand and contract depending upon its temperature. How much expansion can take place for a brass pipe 25.8 m long that experiences temperature changes of 75.2°C?
3.44 cm
5.90 cm
3.69 cm
1.23 cm

Answer 1

Answer on Question #51924-Physics-Field Theory

Expansion joints are used for materials that easily expand and contract depending upon its temperature. How much expansion can take place for a brass pipe 25.8 m long that experiences temperature changes of 75.2°C?

3.44 cm 5.90 cm 3.69 cm 1.23 cm

Solution

Linear expansion formula is

$$l = l _ {0} (1 + \alpha \Delta T),$$

where $l$ is the length after expansion, $l_{0}$ is the length before expansion, $\Delta T$ is the change in temperature, $\alpha$ is the coefficient of linear expansion.

The coefficient of linear expansion for brass is

$$\alpha = 0.000019 \frac{1}{\circ C}.$$

So,

$$\Delta l = l _ {0} \alpha \Delta T = 25.8 \, \mathrm{m} \cdot 0.000019 \frac{1}{\circ \mathrm{C}} \cdot 75.2{}^{\circ} \mathrm{C} = 0.0369 \, \mathrm{m} = 3.69 \, \mathrm{cm}.$$

Answer: 3.69 cm.