Problem 137 - Prealgebra and Introductory Algebra

Question

The boiling point of nitrogen is \(-195.8^{\circ} \mathrm{C},\) and the melting point is \(-209.86^{\circ} \mathrm{C} .\) Find the difference between the boiling point and the melting point of nitrogen.

Step-by-Step Solution

Answer

The difference between the boiling point and the melting point of Nitrogen is \(14.06^{\circ} \mathrm{C}\).

Step 1: Understanding the task

We are given the boiling point and the melting point of Nitrogen, both are in negative degrees Celsius. We are asked to find the difference between these two points.

Step 2: Arranging the values in the correct order

The boiling point of Nitrogen is \(-195.8^{\circ} \mathrm{C}\) and the melting point is \(-209.86^{\circ} \mathrm{C}\). The difference is found by subtracting the smaller value from the larger one in absolute terms to get the positive difference.

Step 3: Perform the subtraction operation

To find this difference, we subtract the lower value (-209.86) from the higher value (-195.8). This is done as follows: \(-195.8 - (-209.86) = -195.8 + 209.86 = 14.06^{\circ} \mathrm{C}\).

Key Concepts

Boiling Point

The boiling point is defined as the temperature at which a substance changes from a liquid to a gas. For nitrogen, this occurs at \(-195.8^{\circ} \mathrm{C}\). It is crucial to understand that each substance has a unique boiling point, influenced by atmospheric pressure.

• The boiling point can vary depending on the pressure of the surroundings, common in different altitudes where pressure changes.
• When calculating differences in boiling points, pay attention to whether you are given values in Celsius or another unit such as Fahrenheit or Kelvin.

Remember, the lower the boiling point, the more volatile the substance at room temperature, as seen with nitrogen which boils far below freezing!

Melting Point

The melting point is the temperature at which a solid transforms into a liquid. For nitrogen, this point is especially low, specifically \(-209.86^{\circ} \mathrm{C}\). This low melting point characteristic means that nitrogen becomes a liquid at temperatures far below the freezing point of water.

• Understanding the melting point is crucial in fields such as chemistry and physics as it helps identify substances and predict their behavior under different conditions.
• In practical applications, knowing the melting point assists in safely handling substances, especially gases like nitrogen that require storage in their liquid state.

Temperature Difference

The concept of temperature difference is simple yet important in understanding changes in thermal energy. It involves calculating the difference in values between two temperatures.

• In our example, to find the temperature difference between nitrogen's boiling point and melting point, we compute the difference by subtracting one temperature from the other.
• Temperature differences do not depend on the absolute scale used (Celsius, Kelvin, etc.), but they require consistent units when performing calculations.

Recognizing a temperature difference can be crucial in processes like chemical reactions, where specific differences might trigger or prevent a reaction.

Negative Numbers

Negative numbers are often situations students fear, but they tell us a lot about the real world, especially in temperature measurement. Both the boiling and melting points of nitrogen are in the negatives, meaning they are below zero degrees Celsius.

• When dealing with negative temperatures, remember: subtracting a negative number is the same as adding its absolute value.
• Understanding negative numbers aids in accurately reading thermometer scales and interpreting scientific data appropriately.

Using examples like nitrogen temperatures helps grasp how to work with negatives in real-life contexts. Knowing you can treat negatives with the same arithmetic rules as positive numbers eases the calculations.