A family/consumer science class is given an assignment in candy-making that requires a sugar mixture to be brought to a "soft-ball" stage \(\left(234-240^{\circ} \mathrm{F}\right)\). A student borrows a thermometer having a range from \(-10^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\) from the chemistry laboratory to do this assignment. Will this thermometer serve the purpose? Explain.

Short Answer

Expert verified
No, the thermometer having a range from \(-10^{\circ} C\) to \(110^{\circ} C\) will not serve the purpose as it does not cover the 'soft-ball' stage temperature range that is \(112.22 - 115.56^{\circ} C\).

Step by step solution

01

Understand the temperature conversion formula

The formula to convert temperature from Fahrenheit to Celsius is given by \(C = (F - 32) \times \frac{5}{9}\). This formula will be used to convert the 'soft-ball' stage temperature range from Fahrenheit to Celsius.
02

Convert the temperature range to Celsius

Apply the conversion formula to the 'soft-ball' stage temperature range (\(234 - 240^{\circ} F\)). The lower limit in Celsius is \((234-32) \times \frac{5}{9} \approx 112.22^{\circ}C\), and the upper limit is \((240-32) \times \frac{5}{9} \approx 115.56^{\circ}C\). So, the temperature range in Celsius is \(112.22 - 115.56^{\circ} C\).
03

Compare the converted temperature range with the thermometer range

The thermometer can measure the temperature from \(-10^{\circ} C\) to \(110^{\circ} C\). Comparing this with the converted 'soft-ball' stage temperature range, \(112.22 - 115.56^{\circ} C\), it is clear that the thermometer does not cover the 'soft-ball' stage temperature range.

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