An aluminum rod 17.400 cm long at $20 ^ { \circ } \mathrm { C }$ is heated to $100 ^ { \circ } \mathrm { C }$ What is its new length? Aluminum has a linear expansion coefficient of $25 \times 10 ^ { - 6 } K ^ { - 1 }$
A) 0.0348 cm
B) 0.348 cm
C) 17.435 cm
D) 17.365 cm

Question

An aluminum rod  17.400 cm long at $20 ^ { \circ } \mathrm { C }$ is heated to $100 ^ { \circ } \mathrm { C }$ What is its new length? Aluminum has a linear expansion coefficient of $25 \times 10 ^ { - 6 } K ^ { - 1 }$
A)  0.0348 cm
B)  0.348 cm
C)  17.435 cm
D)  17.365 cm

Quizplus · Accepted Answer

The new length can be calculated using the formula for linear expansion: $\Delta L = L_0 \alpha \Delta T$, where $\Delta L$ is the change in length, $L_0$ is the original length, $\alpha$ is the coefficient of linear expansion, and $\Delta T$ is the change in temperature. Plugging in the given values: $\Delta L = 17.400 \times 25 \times 10^{-6} \times (100 - 20)$, we find $\Delta L = 0.435 \, \text{cm}$. Adding this to the original length, the new length is $17.400 \, \text{cm} + 0.435 \, \text{cm} = 17.835 \, \text{cm}$. However, given the options, it seems there was a mistake in my calculation. Correctly calculating gives $\Delta L = 17.400 \times 25 \times 10^{-6} \times (100 - 20) = 0.035 \, \text{cm}$, and adding this to the original length gives $17.400 \, \text{cm} + 0.035 \, \text{cm} = 17.435 \, \text{cm}$, which matches option C.

An Aluminum Rod 17 20∘C20 ^ { \circ } \mathrm { C }20∘C

An Aluminum Rod 17 $20 ^ { \circ } \mathrm { C }$