Problem 51 - Prealgebra

Question

The chart shows the temperatures for some of the world's hottest places. To convert from Celsius to Kelvin we use the formula \(y=x+273,\) where \(y\) is the temperature in Kelvin and \(x\) is the temperature in Celsius. Use the formula to answer. CAN'T COPY THE GRAPH The hottest temperature in Al'Aziziyah was 331 Kelvin. Convert this to Celsius.

Step-by-Step Solution

Answer

The temperature in Celsius is 58°C.

Step 1: Understanding the Problem

We need to find the temperature in Celsius given the temperature in Kelvin and the conversion formula. The temperature given for Al'Aziziyah is 331 Kelvin.

Step 2: Analyzing the Formula

The conversion formula from Celsius to Kelvin is given by \(y = x + 273\). To find Celsius \(x\) from Kelvin \(y\), we need to rearrange this formula.

Step 3: Rearrange the Formula

Reorganize the formula to solve for \(x\) (Celsius): \(x = y - 273\).

Step 4: Substitute the Kelvin Value

Substitute the given Kelvin temperature into the rearranged formula: \(x = 331 - 273\).

Step 5: Perform the Calculation

Calculate the value of \(x\): \(x = 331 - 273 = 58\). Thus, the temperature in Celsius is 58°C.

Key Concepts

Celsius to Kelvin Conversion

Converting temperatures from Celsius to Kelvin or vice versa is a fundamental concept in science, particularly in fields like chemistry and physics. This conversion is key because Kelvin is often used in scientific calculations due to its absolute nature, which starts from absolute zero—the coldest possible temperature. In our exercise, the relationship between Celsius and Kelvin is expressed by the formula \[y = x + 273\] where \(y\) is the temperature in Kelvin and \(x\) is the temperature in Celsius. This simple formula allows us to convert any temperature from one scale to the other by either adding or subtracting 273. To convert from Celsius to Kelvin, we add 273. Conversely, to convert from Kelvin to Celsius, we subtract 273 from the Kelvin temperature. This makes the conversion process straightforward and easily applicable in different scenarios.

Rearranging Formulas

Rearranging formulas is a crucial skill in mathematics and science. It allows us to solve for any desired variable in an equation. When we know a formula, and we need a different form of it, rearrangement is the tool we use. For the Celsius to Kelvin conversion, the original formula is \[y = x + 273\] where \(x\) is Celsius and \(y\) is Kelvin. If we need to find the Celsius temperature from a Kelvin value, the goal is to express \(x\) in terms of \(y\). To do this, we subtract 273 from both sides of the equation, giving us: \[x = y - 273\] This rearrangement is key to solving problems that require the temperature in Celsius, as it positions \(x\) on its own, making it easy to calculate.

Step-by-Step Problem Solving

Approaching a problem with a step-by-step method ensures clarity and organization, making it easier to find the solution. This method involves breaking down the problem into manageable parts:

• Understanding the Problem: Identify what is given and what is required. In this case, we have a Kelvin temperature and need to find the corresponding Celsius value.
• Analyzing the Formula: Know the correct formula for the conversion: \(y = x + 273\).
• Rearranging the Formula: Adjust the formula to solve for the unknown variable, resulting in \(x = y - 273\).
• Substituting Values: Insert the given values into the formula. Here, use \(331\) Kelvins.
• Performing Calculations: Execute the arithmetic operations, leading to the result: \(x = 331 - 273 = 58\).

This structured approach not only simplifies problem-solving but also enhances understanding and retention of the concepts involved.

Prealgebra Concepts

Prealgebra sets the foundation for more advanced mathematics. Its concepts include basic operations, simple equations, and fundamental math skills. One important concept is the ability to manipulate equations, which includes combining like terms and performing operations on both sides of an equation. In the context of this temperature conversion, solving \(x = y - 273\) involves subtraction, a fundamental prealgebra operation. Prealgebra also introduces students to the concept of a variable, which symbolizes an unknown value to be found or calculated. Understanding variables and how to work with them is crucial for rearranging and solving equations. This exercise uses these prealgebra concepts to demonstrate how we can convert between different units of measurement by applying basic arithmetic operations.