Question

The temperature in the South Pole during the Antarctic winter is so cold that planes cannot land or take off, effectively leaving the inhabitants of the South Pole isolated for the winter. The average daily temperature at the South Pole in July is \(-59.7{ }^{\circ} \mathrm{C}\). Convert this temperature to degrees Fahrenheit.

Short answer

-59.7 degrees Celsius is equal to -75.46 degrees Fahrenheit.

Step-by-step solution

Understand the Temperature Conversion Formula

To convert Celsius to Fahrenheit, use the formula \( F = \frac{9}{5}C + 32 \), where \( F \) is the temperature in degrees Fahrenheit and \( C \) is the temperature in degrees Celsius.

Substitute the Given Value into the Formula

Substitute \( -59.7{ }^{\circ} \mathrm{C} \) for \( C \) in the conversion formula to get \( F = \frac{9}{5}(-59.7) + 32 \).

Calculate the Temperature in Fahrenheit

First, multiply \( -59.7 \) by \( \frac{9}{5} \) to convert the Celsius to Fahrenheit scale without the offset, and then add 32 to apply the Fahrenheit scale offset: \[ F = \frac{9}{5}(-59.7) + 32 = -107.46 + 32 = -75.46{ }^{\circ} \mathrm{F} \].

Key concepts

Celsius to Fahrenheit

Understanding temperature conversion is essential in many practical situations, including scientific contexts and everyday life. When it comes to converting Celsius to Fahrenheit, one can utilize the formula:

\[ F = \frac{9}{5}C + 32 \]

where \( F \) represents the Fahrenheit temperature, and \( C \) is the temperature in Celsius. This formula is derived from the relationship between the two temperature scales and reflects the ratio of Celsius to Fahrenheit degree increments, as well as the different zero points of the two scales.

Applying the Formula

In our exercise, the frigid average daily temperature of \(-59.7{ }^\circ \mathrm{C}\) at the South Pole needs to be expressed in Fahrenheit. By substituting \( C \) in the formula, we get:

\[ F = \frac{9}{5}(-59.7) + 32 \]

First, we calculate the ratio part to convert the Celsius degrees into Fahrenheit units without the scale’s offset, which results in \(-107.46\). Then, we add the constant \( 32 \) to adjust for the difference in freezing points of water on the two scales. The calculation gives us \(-75.46{ }^\circ \mathrm{F}\), a quite bone-chilling figure that paints a clear picture of the South Pole's harsh winters.

Temperature Scales

Temperature scales serve as a framework for measuring how hot or cold an object is. The Celsius (also called centigrade) and Fahrenheit scales are the two most commonly used temperature scales in daily life and in the sciences.

Celsius Scale

This scale is based on the properties of water, with \(0{ }^\circ\mathrm{C}\) defining the freezing point and \(100{ }^\circ\mathrm{C}\) the boiling point under standard atmospheric conditions. The Celsius scale is widely used around the world and is especially prevalent in scientific applications.

Fahrenheit Scale

The Fahrenheit scale sets the freezing point of water at \(32{ }^\circ\mathrm{F}\) and the boiling point at \(212{ }^\circ\mathrm{F}\), with a standard atmospheric condition. This scale is commonly used in the United States for everyday temperature measurements. The key difference between the scales lies in their starting points and the increments, as they divide the phase change of water differently — the Celsius scale by 100 parts and the Fahrenheit scale by 180 parts.

Understanding these temperature scales is crucial for scientists, researchers, and even chefs, as they influence the interpretation of temperature-related data and the conduct of experiments or cooking.

Chemical Thermodynamics

Chemical thermodynamics is the branch of physical chemistry that deals with the relations between heat changes and other forms of energy, and with the capacity of systems to do work in chemical processes. It plays a critical role in our understanding of the physical properties of substances and the laws that govern energy exchange during chemical reactions.

In chemical thermodynamics, temperature is a core concept as it is directly related to the thermal energy of a system. It's a measure of the average kinetic energy of the molecules in a substance. Lower temperatures correspond to slower molecular motion, while higher temperatures indicate more rapid molecular activity. The behavior of various substances at different temperatures, influenced by the governing laws of thermodynamics, is crucial for everything from designing engines and refrigerators to predicting the behavior of gases, and even understanding the living processes within our cells.

The intricate balance of energy inputs and outputs, enthalpy, entropy, and free energy changes in a system are all examined within this scientific discipline. This not only helps us to predict whether a chemical reaction will occur spontaneously, but also allows for the design of processes that can maximize energy efficiency and yield — essential considerations for any sustainable technological advancement.