By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from $24 ^ { \circ } \mathrm { C } \text { to } - 16 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for this concrete is $1.0 \times$ $10^{ - 5} \mathrm {~K} ^ { - 1 }$
A) 1.5 cm
B) 1.2 cm
C) 0.50 cm
D) 0.72 cm

Question

By what length will a slab of concrete that is originally  18 m  long contract when the temperature drops from $24 ^ { \circ } \mathrm { C } \text { to } - 16 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for this concrete is $1.0 \times$ $10^{ - 5} \mathrm {~K} ^ { - 1 }$
A)  1.5 cm
B)  1.2 cm
C)  0.50 cm
D)  0.72 cm

Quizplus · Accepted Answer

The length change $\Delta L$ can be calculated using the formula $\Delta L = \alpha L_0 \Delta T$, where $\alpha$ is the coefficient of linear expansion, $L_0$ is the original length, and $\Delta T$ is the change in temperature. Here, $\Delta T = -16^\circ C - 24^\circ C = -40^\circ C$, $L_0 = 18 m = 1800 cm$, and $\alpha = 1.0 \times 10^{-5} K^{-1}$. Thus, $\Delta L = 1.0 \times 10^{-5} \times 1800 \times (-40) = -0.72 cm$. The negative sign indicates contraction, so the slab contracts by 0.72 cm.

By What Length Will a Slab of Concrete That Is 24∘C to −16∘C?24 ^ { \circ } \mathrm { C } \text { to } - 16 ^ { \circ } \mathrm { C } ?24∘C to −16∘C?

By What Length Will a Slab of Concrete That Is $24 ^ { \circ } \mathrm { C } \text { to } - 16 ^ { \circ } \mathrm { C } ?$