Using the defined freezing and boiling points of water, make a plot of degrees Fahrenheit versus degrees Celsius on the graph paper provided. Determine the Celsius equivalent of 40 degree F using your graph. The relationship between these two temperature scales is linear (that is it is of the form y = mx + 6). Compute the Celsius equivalent of 40 degree F using this relationship.
The Correct Answer and Explanation is :
To convert temperatures between degrees Fahrenheit (°F) and degrees Celsius (°C), we can use the linear relationship defined by the formula:
[
C = \frac{5}{9}(F – 32)
]
Plotting the Graph
- Identify Key Points:
- Freezing point of water: 0°C = 32°F
- Boiling point of water: 100°C = 212°F
- Create a Table: Here are some key points for both scales:
- (0°C, 32°F)
- (100°C, 212°F)
- (20°C, 68°F)
- (40°C, 104°F)
- Graph Paper: Plot these points on the graph paper, marking the Celsius scale on the vertical axis and the Fahrenheit scale on the horizontal axis. Connect the points with a straight line, indicating the linear relationship.
Determining Celsius Equivalent of 40°F
To find the Celsius equivalent of 40°F using the graph:
- Locate 40°F on the horizontal axis.
- Draw a vertical line up to the point where it intersects the plotted line.
- Read the corresponding value on the vertical axis to find the Celsius temperature.
Calculation Using the Formula
Now, let’s compute the Celsius equivalent of 40°F using the formula:
[
C = \frac{5}{9}(40 – 32)
]
[
C = \frac{5}{9}(8)
]
[
C = \frac{40}{9}
]
[
C \approx 4.44°C
]
Conclusion
The Celsius equivalent of 40°F is approximately 4.44°C. This linear relationship allows for easy conversion between the two temperature scales. The slope ((m)) in the formula indicates how much the Celsius value changes for a given change in Fahrenheit. For example, for every 1°F increase, the Celsius value increases by approximately 0.56°C. This linearity simplifies temperature conversions and provides a clear visual representation when graphed, demonstrating how Celsius and Fahrenheit relate across the temperature spectrum.