To create a new temperature scale, S, where absolute zero is defined as 0°S and the difference between the boiling point and melting point of water is 180°S, we first need to establish a relationship between the Celsius scale and our new scale. Let's break this down step by step.
Understanding the Basics
On the Celsius scale, the melting point of water (T mp,water) is 0°C, and the boiling point of water (T bp,water) is 100°C. The difference between these two temperatures is:
- T bp,water - T mp,water = 100°C - 0°C = 100°C
For our new scale S, we want the difference to be 180°S. This means we need to establish a conversion that reflects this difference while also setting absolute zero at 0°S.
Defining the Conversion Formula
To find the conversion formula from Celsius to S, we can set up a linear relationship. We know:
- At 0°C (the melting point of water), we want 0°S.
- At 100°C (the boiling point of water), we want 180°S.
We can express this relationship with the following linear equation:
S = m * C + b
Where:
- S is the temperature in the new scale.
- C is the temperature in Celsius.
- m is the slope of the line.
- b is the y-intercept.
Finding the Slope and Intercept
To find the slope (m), we can use the two points we have:
- (0, 0) for 0°C and 0°S
- (100, 180) for 100°C and 180°S
The slope m is calculated as:
m = (S2 - S1) / (C2 - C1) = (180 - 0) / (100 - 0) = 180 / 100 = 1.8
Now, we can find the y-intercept (b). Since we know that at 0°C, S is 0, we can directly say:
b = 0
Thus, the conversion formula from Celsius to S is:
S = 1.8 * C
Calculating Boiling and Melting Points in Scale S
Now that we have our conversion formula, we can find the boiling and melting points of water in the S scale:
- For T mp,water (0°C):
S = 1.8 * 0 = 0°S
- For T bp,water (100°C):
S = 1.8 * 100 = 180°S
Final Results
To summarize:
- The conversion formula from Celsius to S is S = 1.8 * C.
- The melting point of water in scale S is 0°S.
- The boiling point of water in scale S is 180°S.
This new temperature scale S effectively maintains the desired properties while providing a clear and logical framework for temperature measurement. If you have any further questions or need clarification on any part of this process, feel free to ask!
