Problem 5 - College Physics

Question

The coldest inhabited village in the world is Oymyakon, a town located in eastern Siberia, where it gets as cold as \(-94^{\circ} \mathrm{F}\). What is this temperature on the Celsius scale?

Step-by-Step Solution

Answer

-94°F is -70°C.

Step 1: Understanding the Relationship between Fahrenheit and Celsius

To convert temperatures between Fahrenheit and Celsius, we use the formula: \( C = \frac{5}{9}(F - 32) \), where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.

Step 2: Substituting the Given Fahrenheit Value

Here, we are given the temperature in Fahrenheit as \(-94^{\circ} \mathrm{F}\). Substitute this value into the formula: \( C = \frac{5}{9}(-94 - 32) \).

Step 3: Calculating the Difference

First, calculate the difference between \(-94\) and \(32\): \(-94 - 32 = -126\). This gives us: \( C = \frac{5}{9}(-126) \).

Step 4: Multiplying by the Fraction

Now, multiply the difference by \( \frac{5}{9} \): \( C = \frac{5}{9} \times (-126) \).

Step 5: Final Calculation of Celsius Temperature

Calculate \( C \): \( C = \frac{5}{9} \times (-126) = -70 \). Thus, the temperature in Celsius is \(-70^{\circ} \mathrm{C}\).

Key Concepts

Celsius scale

The Celsius scale is a widely recognized temperature measurement system used around the world. It is based on two fixed points: the freezing point of water at 0°C and the boiling point of water at 100°C, at standard atmospheric pressure. This scale provides an intuitive way to understand temperature changes in our daily environment.

The Celsius system is part of the metric system and is used in most countries globally. Compared to the Fahrenheit scale, the Celsius scale uses increments that are larger, which can make it easier to mentally calculate changes. For example:

• 10°C is a typical cool autumn day.
• 25°C is a warm summer day.
• -5°C indicates freezing conditions.

Using the Celsius scale can make scientific calculations and comparisons simpler, particularly for those living in regions where the metric system is the standard. The scale, named after the Swedish astronomer Anders Celsius, is a crucial component in fields such as science, engineering, and everyday weather reporting.

Fahrenheit to Celsius formula

The Fahrenheit to Celsius formula is an important tool for converting temperatures between these two scales. The formula is:\[ C = \frac{5}{9}(F - 32) \]where:

• \( C \) is the temperature in degrees Celsius.
• \( F \) is the temperature in degrees Fahrenheit.

This calculation involves two major steps: subtraction and multiplication. First, subtract 32 from the Fahrenheit value. This accounts for the difference in the zero points of the two scales. Then, multiply by \( \frac{5}{9} \) to recalibrate the temperature measurement to the smaller degree increments of the Celsius scale.

Understanding this formula allows one to easily switch between Fahrenheit and Celsius, which is especially useful when comparing temperature conditions across different regions or reading scientific texts. For example, if the temperature is \(-94^{\circ} \mathrm{F}\), applying the formula converts it to \(-70^{\circ} \mathrm{C}\), clearly into the realm of frigid cold.

Cold temperatures in Siberia

Siberia is renowned for its extremely cold temperatures, particularly during the winter months. It is a massive region in Russia known for its harsh climate and vast, often uninhabited landscapes. In places like Oymyakon, the coldest inhabited village on Earth, temperature readings can plunge as low as \(-94^{\circ} \mathrm{F}\), which is equivalent to \(-70^{\circ} \mathrm{C}\).

Such temperatures present numerous challenges and require special adaptations for human survival. Roads and water supplies must be heated, cars need to be kept running or stored in heated garages to prevent freezing, and residents tend to spend most of their time indoors during the coldest periods. Humans and wildlife alike must adapt to this extreme cold.

Despite the cold, Siberia holds significant natural beauty and resources. Its daunting climate contributes to its unique ecosystems and biodiversity, supporting species that thrive in such conditions. Siberia's extreme temperatures are a stark reminder of the planet's climatic diversity and the resilience needed to thrive in some of Earth's most inhospitable regions.