# Temperature in which Celsius and Fahrenheit Scales Coincide

Geometric Solution of the exercise "In which temperature the value of Celsius and Fahrenheit scales coincide"

## Temperature where the value of Celsius and Fahrenheit scales coincide

The image below is the geometric solution of the exercise: “At what temperature the value of Celsius and Fahrenheit scales coincide?”

We want to TC = TF = x. Algebraically, we know that:

TC-0 / 100 = TF-32 / 180

x-0 / 5 = x-32 / 9

x / 5 = x -32 / 9

9x = 5x -(5*32)

9x = 5x -160

9x-5x = -160

4x = -160

x = -40

-40°C=-40°F

## Geometric solution

But there are other possibilities to solve this problem. One of the most elegant, in my point of view, is the geometric solution.

A priori, we must draw on a graph paper a coordinate system. The axis ‘x’ is the energy dissipated in the water, the axis ‘y’ is the temperature.

Perpendicular to the axis ‘x’ we will trace two lines whose energy we know; the temperature of melting and boiling water. On these lines we will mark the points relative to the value of these temperatures in Celsius and Fahrenheit scales. Connecting the dots of each and extending until they meet, we will find the point that belongs to both. We will prolong until the y-axis to see the value.

Figure 1 – Geometric Solution “in which temperature the value of Celsius and Fahrenheit scales coincide”