at what temperature are celsius and fahrenheit equal?

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At what temperature, the Celsius and Fahrenheit scales will read the same ?

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Question

At what temperature, the Celsius and Fahrenheit scales will read the same ?

A−10

o C

B10

o C

C40

o C

D−40

o C Easy Open in App Solution Verified by Toppr

Correct option is D)

The formulas for converting between degree Celsius and degree Fahrenheit are:

°F=(°C∗9/5)+32 °C=(°F−32)∗5/9

To find the temperature when both are equal, we use an old algebra trick and just set ºF = ºC and solve one of the equations.

°C=(°C∗9/5)+32 °C−(°C∗9/5)=32 −4/5∗°C=32 °C=−32∗5/4 °C=−40 °F=(°F∗9/5)+32 °F−(°F∗9/5)=32 −4/5∗°F=32 °F=−32∗5/4 °F=−40

So the temperature when both the Celsius and Fahrenheit scales are the same is −40degrees.

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At what temperature do the Celsius and Fahrenheit scales class 11 physics CBSE

At what temperature do the Celsius and Fahrenheit scales coincide

At what temperature do the Celsius and Fahrenheit scales coincide.

Answer Verified 131.5k+ views 4 likes

Hint: In this question, we have been asked to calculate the temperature at which the Celsius and Fahrenheit scales give the same reading. We know that the Celsius and Fahrenheit scales are two different units of temperature based on different scales. Therefore, we shall discuss both the scales and also understand why the Celsius and Fahrenheit scales are different. Later, we shall discuss the relation between two scales. Therefore, using this relation we will calculate our answer.Formula Used:

( ∘ F−32) 180 = ∘ C 100 (∘F−32)180=∘C100

Complete step by step answer:

Celsius scale was introduced by Andres Celsius. In Celsius scale water is taken as the base and certain standard values are set with respect to water, for example the boiling point of water is 100 degree Celsius and melting point is 0 degree Celsius.

The Fahrenheit scale was introduced by Daniel Gabriel Fahrenheit. According to this scale the boiling point of water is taken as 212 degree Fahrenheit and the melting point as 32 degree Fahrenheit. This gives the exact difference of 180.

The relation between the Fahrenheit and Celsius scale is given by the equation.

⇒ ( ∘ F−32) 180 = ∘ C 100 ⇒(∘F−32)180=∘C100

Now, let us assume that Fahrenheit and Celsius scale coincide at

x ∘ x∘ Therefore, ⇒ ( ∘ x−32) 180 = ∘ x 100 ⇒(∘x−32)180=∘x100 ON solving, We get, ⇒ 5 9 ( ∘ x−32)= ∘ x ⇒59(∘x−32)=∘x Therefore, ⇒x=−40 ∘ ⇒x=−40∘

Therefore, Celsius and Fahrenheit scale coincide at -40 degrees.Note:

The difference between both scales is the base measurement. The Celsius scale has a melting point of water as 100 degrees and Fahrenheit scale has 32 degrees. The other factor differentiating them is the acceptance. The Celsius scale is simple and widely used. The Fahrenheit scale is used in the USA and few other countries. The Celsius scale is not accepted in other regions where the Kelvin is used as a measurement unit of temperature. All the scales are convertible to one another.

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What Temperature Does Fahrenheit Equal Celsius?

There is a point on the Fahrenheit and Celsius scales where the temperatures in degrees are equal. See the simple algebraic method to find the answer

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What Temperature Does Fahrenheit Equal Celsius?

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By Anne Marie Helmenstine, Ph.D.

Updated on January 27, 2020

Celsius and Fahrenheit are two important temperature scales. The Fahrenheit scale is used primarily in the United States, while Celsius is used throughout the world. The two scales have different zero points and the Celsius degree is bigger than the Fahrenheit.

However, there is one point on the Fahrenheit and Celsius scales where the temperatures in degrees are equal. This is -40 °C and -40 °F. If you can't remember the number, there is a simple algebraic method to find the answer.

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Difference Between Fahrenheit and Celsius

Key Takeaways: When Does Fahrenheit Equal Celsius?

Celsius and Fahrenheit are two temperature scales.

The Fahrenheit and Celsius scales have one point at which they intersect. They are equal at -40 °C and -40 °F.

The simple method to find when two temperature scales are equal to each other is to set the conversion factors for the two scales equal to each other and solve for temperature.

Setting Fahrenheit and Celsius Equal

Rather than converting one temperature to another (which is not helpful because it assumes you already know the answer), you can set degrees Celsius and degrees Fahrenheit equal to each other using the conversion formula between the two scales:

°F = (°C * 9/5) + 32

°C = (°F - 32) * 5/9

It does not matter which equation you use; simply use x instead of degrees Celsius and Fahrenheit. You can solve this problem by solving for x:

°C = 5/9 * (°F - 32)

x = 5/9 * (x - 32) x = (5/9)x - 17.778

1x - (5/9)x = -17.778

0.444x = -17.778

x = -40 degrees Celsius or Fahrenheit

Working using the other equation, you get the same answer:

°F = (°C * 9/5) + 32

°x - (°x * 9/5) = 32

-4/5 * °x = 32 °x = -32 * 5/4 x = -40°

More About Temperature

You can set two scales equal to each other to find when any of them intersect. Sometimes it's easier to just look up the equivalent temperature. This handy temperature conversion scale may help you out.

You can also practice converting between temperature scales:

Fahrenheit to Celsius

Celsius to Fahrenheit

Celsius Versus Centigrade

Source : www.thoughtco.com