Lecture Notes: Celsius and Fahrenheit Temperature Equivalence

Overview

• The lecture discusses the point where Celsius and Fahrenheit temperatures are equal.
• It explains the mathematical calculation to find the temperature where both degree Celsius and degree Fahrenheit are the same.

Key Concepts

Temperature Equivalence

• Objective: To determine the temperature at which degrees Celsius equals degrees Fahrenheit.

• Equation Used: Relationship between Celsius (C) and Fahrenheit (F) temperatures is given by:

  [ F = \frac{9}{5}C + 32 ]

Mathematical Calculation

1. Assumption: At temperature ( t ), ( F = C ).

2. Equation Setup:

   • Substitute ( F ) for ( C ) in the equation:

     [ t = \frac{9}{5}t + 32 ]

3. Solving the Equation:

   • Rearrange to solve for ( t ):

     [ t - \frac{9}{5}t = 32 ]

   • Convert to a common factor:

     [ \frac{5t - 9t}{5} = 32 ]

   • Simplify:

     [ -\frac{4t}{5} = 32 ]

   • Cross-multiply and solve:

     [ -4t = 5 \times 32 ]

   • Continue solving:

     [ -4t = 160 ]

4. Final Solution:

   • Divide both sides by -4:

     [ t = -40 ]

   • Thus, (-40°C = -40°F).

Conclusion

• Result: The temperature at which Celsius and Fahrenheit are equal is (-40°).
• Additional Note: At all other temperatures, Celsius and Fahrenheit are not equal (e.g., (0°C = 32°F)).

Closing Remarks

• Encouragement to engage with questions or comments.
• Reminder to like, share, and subscribe to the channel for more content.