To find the temperature on the W scale that corresponds to 239°C on the Celsius scale, we need to establish a relationship between the two temperature scales. Since the W scale is linear, we can use the freezing and boiling points of water on both scales to create a conversion formula.
Understanding the Temperature Scales
First, let's identify the key points on both scales:
- On the Celsius scale, the freezing point of water is 0°C and the boiling point is 100°C.
- On the W scale, the freezing point of water is 39°W and the boiling point is 239°W.
Setting Up the Conversion
We can set up a linear equation based on the two known points. The relationship between the Celsius temperature (C) and the W temperature (W) can be expressed as follows:
Let’s denote the freezing point of water as \(C_f = 0°C\) and \(W_f = 39°W\), and the boiling point as \(C_b = 100°C\) and \(W_b = 239°W\).
Using these points, we can find the slope (m) of the line that connects these two points:
m = (W_b - W_f) / (C_b - C_f) = (239 - 39) / (100 - 0) = 200 / 100 = 2.
Finding the Intercept
Next, we need to find the y-intercept (b) of the linear equation. We can use one of the points to solve for b. Using the freezing point:
39 = 2(0) + b, thus b = 39.
Formulating the Equation
The linear equation that relates Celsius to W is:
W = 2C + 39.
Calculating the W Temperature
Now, we can substitute 239°C into our equation to find the corresponding W temperature:
W = 2(239) + 39 = 478 + 39 = 517°W.
Final Thoughts
It seems there was a misunderstanding in your question regarding the conversion. The calculated temperature on the W scale corresponding to 239°C is actually 517°W, not 78°W. If you have any further questions or need clarification on any part of this process, feel free to ask!
