A hole in a brass plate has a diameter of 1.200 cm at $20 ^ { \circ } \mathrm { C }$ What is the diameter of the hole when the plate is heated to $220 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for brass is $19 \times 10 ^ { - 6 } K ^ { - 1 }$
A) 1.205 cm
B) 1.195 cm
C) 1.210 cm
D) 1.200 cm

Question

A hole in a brass plate has a diameter of  1.200 cm at $20 ^ { \circ } \mathrm { C }$ What is the diameter of the hole when the plate is heated to $220 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for brass is $19 \times 10 ^ { - 6 } K ^ { - 1 }$
A)  1.205 cm
B)  1.195 cm
C)  1.210 cm
D)  1.200 cm

Quizplus · Accepted Answer

The diameter of the hole increases with temperature due to thermal expansion. The change in diameter can be calculated using the formula $\Delta L = L_0 \alpha \Delta T$, where $\Delta L$ is the change in length (diameter in this case), $L_0$ is the original length, $\alpha$ is the coefficient of thermal expansion, and $\Delta T$ is the change in temperature. Given $L_0 = 1.200$ cm, $\alpha = 19 \times 10^{-6} K^{-1}$, and $\Delta T = 220 - 20 = 200$°C, the change in diameter is $1.200 \times 19 \times 10^{-6} \times 200$, which results in an increase, making the new diameter approximately 1.205 cm.

A Hole in a Brass Plate Has a Diameter of 20∘C20 ^ { \circ } \mathrm { C }20∘C

A Hole in a Brass Plate Has a Diameter of $20 ^ { \circ } \mathrm { C }$