Question

At the Amundsen-Scott South Pole base station in Antarctica, when the temperature is \(-100.0^{\circ} \mathrm{F}\) , researchers who live there can join the 4300 \(\mathrm{Club}^{\prime \prime}\) by stepping into a sauna heated to \(200.0^{\circ} \mathrm{F}\) then quickly running outside and around the pole that marks the South Pole. What are these temperatures in \(^{\circ} \mathrm{C} ?\) What are these temperatures in \(\mathrm{K}\) ? If you measured the temperatures only in \(^{\circ} \mathrm{C}\) and \(\mathrm{K}\) , can you become a member of the \(" 300 \mathrm{Club}^{\prime \prime}\) (that is, is there a 300 .-degree difference between the temperature extremes when measured in \(^{\circ} \mathrm{C}\) and \(\mathrm{K}\) )?

Short answer

The temperatures in Celsius are -73.3°C and 93.3°C, and in Kelvin, they are 199.85 K and 366.45 K. The difference between the temperature extremes is 166.6 in both Celsius and Kelvin, which is not 300. Thus, a researcher cannot become a member of the 300 Club when measuring temperatures only in Celsius and Kelvin.

Step-by-step solution

Convert Fahrenheit to Celsius

To convert Fahrenheit to Celsius, we use the formula: \[Celsius = \frac{5}{9} (Fahrenheit - 32)\] We are given two Fahrenheit temperatures: 1. -100.0°F 2. 200.0°F Let's convert these to Celsius: 1. \(Celsius_1 = \frac{5}{9} (-100.0 - 32)\) 2. \(Celsius_2 = \frac{5}{9} (200.0 - 32)\)

Calculate Celsius Temperatures

Calculate the Celsius temperatures using the converted temperatures formula: 1. \(Celsius_1 = \frac{5}{9} (-132) = -73.3°C\) 2. \(Celsius_2 = \frac{5}{9} (168) = 93.3°C\)

Convert Celsius to Kelvin

To convert Celsius to Kelvin, we use the formula: \[Kelvin = Celsius + 273.15\] We have two Celsius temperatures: 1. -73.3°C 2. 93.3°C Let's convert these to Kelvin: 1. \(Kelvin_1 = -73.3 + 273.15\) 2. \(Kelvin_2 = 93.3 + 273.15\)

Calculate Kelvin Temperatures

Calculate the Kelvin temperatures using the converted temperatures formula: 1. \(Kelvin_1 = 199.85 K\) 2. \(Kelvin_2 = 366.45 K\)

Check for a 300-degree difference

To see if a researcher can become a member of the 300 Club, we need to check if the difference in the temperature extremes is 300 when measured in Celsius and Kelvin: 1. Celsius Difference: |93.3 - (-73.3)| = 166.6 2. Kelvin Difference: |366.45 - 199.85| = 166.6 The difference between the temperature extremes is the same in Celsius and Kelvin (166.6), but it is not 300. Therefore, a researcher cannot become a member of the 300 Club when measuring temperatures only in Celsius and Kelvin.

Key concepts

Celsius

The Celsius scale is a metric system temperature measurement used worldwide. Named after Swedish astronomer Anders Celsius, it uses the freezing and boiling points of water as its reference points. Water freezes at 0°C and boils at 100°C. This scale is advantageous due to its ease of use and straightforward nature.

In the exercise, we are converting temperatures from Fahrenheit, and calculating using the formula:

• \(Celsius = \frac{5}{9} (Fahrenheit - 32)\)

This formula helps to translate the values to the Celsius scale. For instance, sufficiently extreme temperatures like -100.0°F were converted to -73.3°C, positioning this as a practical scale in scientific practices.

Fahrenheit

Fahrenheit is one of the temperature measurement systems, mainly used in the United States. It was developed by Gabriel Fahrenheit and uses 32°F as the freezing point and 212°F as the boiling point of water. This system can be more suitable for ambient temperatures rather than extreme settings.

When comparing Fahrenheit to other scales like Celsius or Kelvin, convert this to observe global temperature readings accurately. For example, in the exercise:

• \(-100.0^{\circ} \text{F} \to -73.3^{\circ} \text{C}\).
• \(200.0^{\circ} \text{F} \to 93.3^{\circ} \text{C}\).

These conversions are crucial for researchers at locations like the Amundsen-Scott South Pole to calibrate scientific equipment accurately.

Kelvin

Kelvin is the SI unit for temperature, primarily used in scientific settings that require absolute temperature measurements. William Thomson, also known as Lord Kelvin, introduced this scale grounded on an absolute zero point – the theoretical temperature where particles cease motion. This scale does not go below 0 K, correlating directly with Celsius:

• \(Kelvin = Celsius + 273.15\).

This direct relationship is beneficial for converting between scales, especially for exercises similar to the one at the South Pole station, where a temperature can be reliably calculated:

• -73.3°C becomes 199.85 K
• 93.3°C becomes 366.45 K

These conversions allow researchers to utilize measurements in their absolute form.

Amundsen-Scott South Pole

The Amundsen-Scott South Pole Station sits at the most southern point of our planet. Characterized by having perhaps the most extreme environments on Earth, the base experiences frigid temperatures, often staying well below freezing, creating a demanding setting for research.

Scientists stationed here often encounter temperatures like -100°F. Surviving and investigating in such conditions demand precise temperature measurements across various scales, including Celsius and Kelvin, to understand local climates and test equipment against these harsh conditions.
The location also spark interesting aspects of human endurance and adaptation to severe cold, often depicted through cultural activities like the famous 300 Club challenge.

300 Club

The 300 Club is a unique activity practiced at the Amundsen-Scott South Pole Station. This club requires individuals to experience a temperature span of 300 degrees Fahrenheit quickly. Participants typically jump from a 200°F sauna directly into a blizzard-like -100°F temperature for the thrill and adventure.

In scientific terms:

• This activity utilizes temperature conversion and differences, but in Celsius, the difference only spans 166.6°C.
• Similarly, in Kelvin, the disparity measures 166.6 K as well.

Even if not meeting the 300-degree mark in Celsius or Kelvin, the challenge stands as a symbolic exercise in human endurance and resilience against extreme climates.