Question

The lowest air temperature recorded on Earth is \(-129^{\circ} \mathrm{F}\) in Antarctica. Convert this temperature to the Celsius scale.

Short answer

Answer: The lowest air temperature recorded on Earth in Antarctica is -89°C.

Step-by-step solution

Write down the provided information

The lowest air temperature recorded on Earth is \(-129^{\circ} \mathrm{F}\) in Antarctica.

Write down the formula for converting Fahrenheit to Celsius

\(C = \frac{5}{9}(F - 32)\)

Plug in the given Fahrenheit temperature

We are given \(F = -129^{\circ} \mathrm{F}\). Now, let's substitute this value into the formula: \(C = \frac{5}{9}(-129 - 32)\)

Subtract 32 from the Fahrenheit temperature

To find the difference in Fahrenheit, subtract 32 from the given value: \(-129 - 32 = -161\)

Multiply by the fraction \(\frac{5}{9}\)

Now, we just need to multiply this difference by the fraction \(\frac{5}{9}\): \(C = \frac{5}{9}(-161)\)

Calculate the temperature in Celsius

Now, let's calculate the temperature in Celsius by performing the multiplication: \(C = -89^{\circ} \mathrm{C}\) So, the lowest air temperature recorded on Earth in Antarctica, when converted to the Celsius scale, is \(-89^{\circ} \mathrm{C}\).

Key concepts

Fahrenheit to Celsius Conversion

Understanding how to convert temperatures from the Fahrenheit scale to the Celsius scale is a fundamental skill in both daily life and physics. The formula that connects these two temperature scales is expressed as \(C = \frac{5}{9}(F - 32)\). To convert temperatures, one starts by subtracting 32 from the Fahrenheit temperature. This number comes from the offset between the freezing points of water on both scales: 32°F is equivalent to 0°C. The remaining difference in temperature is then multiplied by \(\frac{5}{9}\), because the Celsius scale is based on a decimal system where the boiling and freezing points of water are 100 degrees apart, compared to 180 degrees on the Fahrenheit scale (212°F - 32°F = 180°F). Thus, the \(\frac{5}{9}\) ratio represents the conversion factor needed to translate the Fahrenheit increments to Celsius increments.

For example, let's convert the record lowest air temperature on Earth, \(-129^\circ \mathrm{F}\), to Celsius. We subtract 32, resulting in \(-129 - 32 = -161\). This figure is then multiplied by \(\frac{5}{9}\), yielding a temperature of \(-89^\circ \mathrm{C}\) in Celsius. It's crucial for students to follow the correct order of operations in the formula and accurately perform each step to ensure a correct conversion.

Temperature Scales

Temperature scales are tools used to measure how hot or cold something is. The most commonly used scales are Celsius and Fahrenheit, each with its own applications and history. The Celsius scale, originally known as the centigrade scale, was developed in the 18th century and is used in the metric system. It is based on the properties of water, with 0°C denoting the freezing point and 100°C the boiling point, at sea level. This scale is widely used around the world, especially in scientific contexts.

The Fahrenheit scale, on the other hand, was developed in the early 18th century by Daniel Gabriel Fahrenheit. It sets the freezing point of water at 32°F and the boiling point at 212°F. This scale is mostly used in the United States and a few other countries. When it comes to physics, the Kelvin scale is also important. It is the SI unit for temperature and starts at 0 K, which is absolute zero—the temperature where all thermal motion ceases in the classical description of thermodynamics.

Each scale has its own application, with scientists typically using Kelvin or Celsius, while Fahrenheit is more common in everyday weather reports in the U.S. Understanding how to interconvert between these scales is essential for data comparison and scientific communication.

Physics Problem-Solving

Physics problem-solving is a skill that encompasses understanding concepts, applying formulas, and systematically working through calculations. A good physics problem-solver will start by analyzing the given information and identifying what needs to be found. Once the problem is understood, the next step involves formulating a strategy. In our example of temperature conversion, the strategy involved applying a specific conversion formula.

Other common strategies include breaking a problem down into smaller parts, using diagrams to visualize the problem, or applying conservation laws. It's essential to work methodically, proceeding step by step and checking work at each stage to prevent errors. In our example, each step of the conversion was clearly outlined and executed in sequence, which is a typical approach to problem-solving in physics.

Focusing on each step individually can help prevent feeling overwhelmed, especially with complex problems. Additionally, always review your final answer to ensure it makes sense in the context of the question. In our conversion exercise, once we derived the Celsius value, we compared it to known values (like the freezing and boiling point of water) to affirm that our answer was reasonable.