What is the maximum volume expansion coefficient of ?

Homework Statement

You are building a device for monitoring ultracold environments. Because the device will be used in environments where its temperature will change by 211°C in 2.99s, it must have the ability to withstand thermal shock (rapid temperature changes). The volume of the device is 3.00⋅10−5m3, and if the volume changes by 1.00⋅10−7m3 in a time interval of 7.15s, the device will crack and be rendered useless. What is the maximum volume expansion coefficient that the material you use to build the device can have?

ΔT = 211 °C
V0 = 3.00⋅10-5 m3
ΔV = 1.00⋅10-7 m3
β = ?

ΔV = β(ΔT)V0

The Attempt at a Solution

It seems like I am given everything to calculate the volume expansion coefficient, β.

I am not sure how the time limit of 2.99 s comes into play here if it takes us longer than 2.99 s for the temperature to change so the risk of thermal shock is avoided and seems like extra information and not something I need to take in account. I realize I may be wrong and want to understand why.

I rearranged to solve β

β = (ΔV)/(ΔT)(V0)

β = (1.00⋅10-7 m3)/(211 °C)(3.00⋅10-5 m3)

β = 1.5798⋅10-5

I submitted this problem to my online homework and I was incorrect.

Any help would be appreciated.

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