Problem 206 - Chemistry Matter and Change

Question

Making Candy A recipe for pralines calls for the candy mixture to be heated until it reaches the "soft ball" stage, at about \(236^{\circ} \mathrm{F}\) . Can a Celsius thermometer with a range of \(-10\) to \(110^{\circ} \mathrm{C}\) be used to determine when the "soft ball" stage is reached? (Chapter 2\()\)

Step-by-Step Solution

Answer

No, the thermometer cannot measure \(113.33^{\circ} \mathrm{C}\).

Step 1: Understanding the Problem

We need to determine if a Celsius thermometer can measure at least up to the temperature that's equal to the "soft ball" stage in Fahrenheit, which is given as \(236^{\circ} \mathrm{F}\). The Celsius thermometer in question measures between \(-10\) to \(110^{\circ} \mathrm{C}\).

Step 2: Convert Fahrenheit to Celsius

The conversion from Fahrenheit to Celsius is done using the formula: \[ C = \frac{5}{9}(F - 32) \] Plug in \(F = 236\) into the formula: \[ C = \frac{5}{9}(236 - 32) \] Simplify to find the Celsius equivalent.

Step 3: Simplify the Conversion Calculation

First, calculate \(236 - 32 = 204\). Then, apply the conversion: \[ C = \frac{5}{9} \times 204 = \frac{1020}{9} \approx 113.33 \] This means that \(236^{\circ} \mathrm{F} \approx 113.33^{\circ} \mathrm{C}\).

Step 4: Compare with Thermometer Range

The Celsius thermometer range is \(-10\) to \(110^{\circ} \mathrm{C}\). Compare \(113.33^{\circ} \mathrm{C}\) with the maximum the thermometer can read (\(110^{\circ} \mathrm{C}\)).

Step 5: Conclusion

Since \(113.33^{\circ} \mathrm{C}\) is greater than \(110^{\circ} \mathrm{C}\), the thermometer cannot measure the temperature of the "soft ball" stage.

Key Concepts

Fahrenheit to Celsius

Temperature conversion is a handy skill, especially when recipes or scientific data involve different units. To convert from Fahrenheit (°F) to Celsius (°C), we use the formula:

• Formula: \( C = \frac{5}{9}(F - 32) \)
• Step-by-step usage: Start by subtracting 32 from the Fahrenheit value.
• Next, multiply the result by \( \frac{5}{9} \) to get the Celsius equivalent.

For example, to convert \(236^{\circ} \mathrm{F}\), you would first subtract 32, getting 204. Then multiply 204 by \(\frac{5}{9}\), resulting in approximately \(113.33^{\circ} \mathrm{C}\). This simple math gives us the ability to understand temperatures in different scales which is crucial for following recipes or when working with various scientific instruments. Being familiar with both scales can be quite practical for anyone working with temperature-sensitive tasks.

thermometer range

Thermometers have specific limits within which they can accurately measure temperature, called their range. The range of a thermometer tells us both the lowest and highest temperatures it can detect.

• The given thermometer's range is from \(-10^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\).
• This means it can only provide accurate readings within these bounds.
• If a temperature exceeds this range, like the \(113.33^{\circ} \mathrm{C}\) needed for the "soft ball" stage of candy making, the thermometer will not be able to provide a correct reading.

Thus, knowing the range is essential to ensure accuracy, and potentially opting for another tool if the required measurement exceeds the thermometer's limits.

measurement accuracy

Accuracy in temperature measurement is crucial whether you are cooking candy or running a scientific experiment. Accuracy refers to how close a measured value is to the actual true value.

• Instruments outside their range can compromise accuracy.
• For the pralines recipe, if the thermometer reads up to \(110^{\circ} \mathrm{C}\), it cannot accurately measure \(113.33^{\circ} \mathrm{C}\), leading to unreliable results.
• If you use a thermometer with a restricted range, you risk inaccuracies that may ruin the recipe, as cooking is a precision task.

To maintain accuracy, always ensure that the tool used matches the requirements of the task. For candy making, a thermometer that can measure up to a higher range is necessary to accurately determine when the pralines reach the soft ball stage.