Problem 52 - 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 Kebili, Tunisia, was 328 Kelvin. Convert this to Celsius.

Step-by-Step Solution

Answer

The Celsius temperature is 55°C.

Step 1: Understanding the Conversion Formula

The formula to convert from Celsius to Kelvin is given by \( y = x + 273 \), where \( y \) is the temperature in Kelvin, and \( x \) is the temperature in Celsius. To find the Celsius temperature from Kelvin, we need to solve for \( x \).

Step 2: Rearrange the Formula

To find the temperature in Celsius \( x \), rearrange the conversion formula: \( x = y - 273 \).

Step 3: Substitute the given Kelvin Temperature

Substitute the given Kelvin temperature into the rearranged formula. Here, \( y = 328 \). Substitute to get: \( x = 328 - 273 \).

Step 4: Calculate the Celsius Temperature

Perform the subtraction in the equation. Calculate: \( x = 328 - 273 = 55 \).

Step 5: Final Result

The calculation shows that the temperature in Celsius is \( 55 \degree C \).

Key Concepts

Celsius to Kelvin

When converting temperatures from Celsius to Kelvin, the process is straightforward and requires a simple mathematical formula. The foundational principle is that Kelvin and Celsius scales measure temperature using different starting points. The Kelvin scale is set such that 0 Kelvin is absolute zero, the coldest possible temperature, which is equivalent to -273.15 degrees Celsius.

To express this conversion into a formula, we use:

• Formula: \( y = x + 273 \)
• Variable meanings: \( y \) is the temperature in Kelvin, \( x \) is the temperature in Celsius.

By plugging the Celsius temperature into this formula, we get its Kelvin equivalent. This simple addition (adding 273) stems from the reason that 0 degrees Celsius is naturally aligned with 273 Kelvin (since water freezes at these points on each respective scale).

Therefore, giving you a systematic way to ensure every temperature conversion remains consistent and accurate, even under test conditions.

Kelvin to Celsius

Converting a temperature from Kelvin back to Celsius is quite similar in execution, but with a reverse operation. This conversion is necessary, particularly when encountering scientific data expressed in Kelvin but applied in a context requiring Celsius, such as weather reports or everyday temperature discussions.

To achieve this conversion, the formula is slightly rearranged from the original Celsius to Kelvin version:

• Formula: \( x = y - 273 \)
• Variable meanings: \( x \) is the temperature in Celsius, \( y \) is the temperature in Kelvin.

By subtracting 273 from the Kelvin temperature, you find its Celsius counterpart. The subtraction accounts for the difference in the starting point of the two scales and corrects for the fact that absolute zero (0 Kelvin) is the baseline.

In our example exercise, we demonstrated this conversion process by taking a temperature from Kebili, Tunisia, which was recorded at 328 Kelvin, then converting it to 55 degrees Celsius. This result illustrates why understanding this conversion is crucial for interpreting real-world measurements.

Mathematical Formulas

Mathematical formulas are powerful tools used to articulate relationships between different variables clearly and precisely. In temperature conversion, these formulas simplify complex concepts, allowing direct computation without intense theoretical analysis.

Key points on their importance include:

• They provide a consistent process for converting temperatures between scales.
• They establish a relationship between Celsius and Kelvin through constants (in our case, 273).
• Formulas act as bridges that translate raw data into usable information, quickening the task.

The formula \( y = x + 273 \) embodies these principles by establishing a direct link between temperatures in Celsius and Kelvin. Simultaneously, the rearranged formula \( x = y - 273 \) is its counterpart, enabling smooth reversal of the procedure—demonstrating the versatility of mathematical formulas.

Understanding and applying these formulas requires only basic arithmetic, making temperature conversions accessible and manageable for anyone, whether for educational exercises or real-world applications.