Problem 10 - Algebra A Combined Function

Question

The freezing point of water is \(0^{\circ}\) Celsius. The boiling point of water is \(100^{\circ}\) Celsius. Write an inequality statement using \(<\) or \(>\) comparing the numbers 0 and \(100 .\)

Step-by-Step Solution

Answer

0 < 100

Step 1: Identify the Values

The problem gives us two specific temperatures: the freezing point of water, which is \(0^{\circ}\) Celsius, and the boiling point of water, which is \(100^{\circ}\) Celsius.

Step 2: Understand the Comparison

We need to compare these two values using the inequality symbols \(<\) or \(>\). This involves determining which temperature is colder and which is hotter.

Step 3: Formulate the Inequality

Since \(0^{\circ}\) Celsius is the freezing point and \(100^{\circ}\) Celsius is the boiling point, \(0^{\circ}\) is less than \(100^{\circ}\). Therefore, we can write the inequality as \(0 < 100\).

Key Concepts

Freezing Point

The freezing point is a fundamental concept in understanding temperature scales and thermal transitions. When we talk about the freezing point of water, we're referring to the temperature at which liquid water transitions into solid ice. This happens at 0 degrees Celsius, which is a critical reference point in various scientific and everyday applications.
Understanding freezing points is essential because:

• It helps in predicting weather conditions, including potential frost and snow.
• It is crucial in cooking and food preservation techniques, such as freezing food for long-term storage.
• Chemists and engineers rely on it to design materials and systems that must endure low temperatures.

In the Celsius scale, 0 degrees is a common benchmark. It acts as a zero point from which other temperature measurements can be compared, like boiling and melting points.

Boiling Point

The boiling point is another key temperature concept and represents the temperature at which a liquid turns into a gas. For water, this point is at 100 degrees Celsius under standard atmospheric pressure. This is also an important reference in many scientific and practical scenarios.
Boiling points matter because:

• They are critical in cooking, where liquid water needs to transform into vapor, such as in boiling pasta or making soups.
• They play a significant role in industrial processes, such as distillation, which separates components based on different boiling points.
• In environmental sciences, boiling points help understand and predict evaporation rates in bodies of water.

At 100 degrees Celsius, water bubbles and evaporates rapidly, an essential property utilized in everyday life from simple meal preparations to complex chemical analyses.

Temperature Comparison

Comparing temperatures involves using mathematical inequalities to understand the relationship between different thermal values. This can be done using symbols such as "<", which means "less than", and ">", which means "greater than".
In the context of the original problem, we compare the freezing point (0 degrees Celsius) and the boiling point (100 degrees Celsius) of water. The mathematical inequality for these two points is:

• 0 degrees Celsius < 100 degrees Celsius
  This inequality simply states that the freezing point is less than the boiling point.

Knowing how to compare temperatures is useful for:

• Making quick decisions on appropriate clothing for weather conditions.
• Determining the right settings for appliances like ovens and fridges.
• Analyzing data in scientific research, where temperature differences can indicate chemical changes or physical transformations.

Mastering temperature comparisons allows us to understand and predict many phenomena that occur with changes in temperature.