Question

When the temperature is \(0^{\circ} \mathrm{C},\) is it also \(0^{\circ} \mathrm{F} ?\) Explain.

Short answer

At \(0^{\circ} \mathrm{C}\), the temperature is \(32^{\circ} \mathrm{F}\), not \(0^{\circ} \mathrm{F}\).

Step-by-step solution

Understanding Temperature Conversion

To know whether the temperature is the same in Fahrenheit as it is in Celsius, we can use the temperature conversion formula: \[ F = \frac{9}{5}C + 32 \]. We'll substitute the Celsius value, which is given as \(0^{\circ} \mathrm{C}\), into this formula to find the corresponding Fahrenheit value.

Substituting Celsius into the Formula

Substitute \(C = 0\) into the conversion formula: \[ F = \frac{9}{5}(0) + 32 \]. This simplifies to \[ F = 0 + 32 \].

Solving the Equation

Simplifying further, we find:\[ F = 32 \]. Therefore, when the temperature is \(0^{\circ} \mathrm{C}\), it is actually \(32^{\circ} \mathrm{F}\), not \(0^{\circ} \mathrm{F}\).

Conclusion

The temperature \(0^{\circ} \mathrm{C}\) corresponds to \(32^{\circ} \mathrm{F}\). Therefore, the statement that \(0^{\circ} \mathrm{C}\) is \(0^{\circ} \mathrm{F}\) is incorrect.

Key concepts

Celsius to Fahrenheit Conversion

Temperature conversion between Celsius and Fahrenheit is a common task. Understanding the conversion process can make it much easier. The main formula to convert Celsius to Fahrenheit is:\[ F = \frac{9}{5}C + 32 \]Here, \(F\) represents the Fahrenheit temperature and \(C\) represents the Celsius temperature. The formula is designed to account for the different starting points and scales of the two temperature systems. Celsius and Fahrenheit differ primarily by the way they are scaled: the Fahrenheit scale has a different zero point and step size between degrees compared to the Celsius scale.For example, to convert \(0^{\circ} \mathrm{C}\) to Fahrenheit, you would plug 0 into the formula:

• Multiply 0 by \(\frac{9}{5}\), which is 0.
• Add 32 to the result to obtain 32.

This calculation shows that \(0^{\circ} \mathrm{C}\) is equivalent to \(32^{\circ} \mathrm{F}\). Thus, understanding this formula is key to converting any Celsius temperature to Fahrenheit.

Mathematical Problem Solving

Solving a math problem systematically improves the likelihood of arriving at the correct answer. For our temperature conversion problem, we started with a clear understanding of what is needed: conversion from Celsius to Fahrenheit. Then, we identified the right formula for the task.The steps are crucial:

• Identify what is given: here, a temperature in Celsius.
• Use the relevant conversion formula.
• Substitute the given values into the formula.
• Simplify the mathematical expression to reach the answer.

With any problem, breaking down the steps and tackling them one by one helps prevent errors and ensures clarity of thought. In this case, substituting 0 into the formula and simplifying stepwise led to the correct solution: \(32^{\circ} \mathrm{F}\). Problem-solving in this manner is not just about finding the answer; it’s about practicing logical thought processes.

Understanding Temperature Scales

The Celsius and Fahrenheit scales are both used to measure temperature, but they work quite differently. Celsius is based on the metric system, while Fahrenheit was developed earlier and is still in wide use in places like the United States. Celsius is oriented to the freezing and boiling points of water:

• 0 degrees for the freezing point.
• 100 degrees for the boiling point.

Fahrenheit, on the other hand, defines these points at 32 and 212 degrees, respectively. These differing definitions mean that the two scales have different intervals and zero points, which is why conversion is necessary. Understanding both scales is important not just for scientific purposes, but also for everyday tasks like reading weather reports or cooking. Each scale provides a different perspective, but with the proper conversion, they can be related accurately. This highlights the importance of having a reliable method, like the conversion formula, to bridge the two systems.