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Question: Which of the following temperatures is the same on the Centigrade and Fahrenheit scales? A. \(0^\c...

Which of the following temperatures is the same on the Centigrade and Fahrenheit scales?
A. 0∘0^\circ
B. 40∘40^\circ
C. −273∘- 273^\circ
D. −40∘- 40^\circ

Explanation

Solution

Celsius is also called a centigrade scale which is based on 0∘C0^\circ {\rm{C}} for the freezing point of water and100∘C100^\circ {\rm{C}} the boiling point of water. The Fahrenheit scale takes32∘F32^\circ {\rm{F}} as a freezing point and 212∘F212^\circ {\rm{F}} as a boiling point of water.

Complete step by step answer:
We know, both Fahrenheit and Celsius scales are used to measure the temperature. The temperature in Celsius scale will be shown in degree Celsius whereas the temperature Fahrenheit scale will be expressed in degree Fahrenheit. Also, the relation between both Fahrenheit and Celsius scales is in proportion, i.e. both have different freezing points of water, and both follow the varied unit difference between each scale. When the temperature in Celsius increases, it's Fahrenheit equivalent temperature will also be so high. When the temperature in Celsius scales decreases, its Fahrenheit equivalent temperature will also be below. From both Celsius and Fahrenheit scales (Fahrenheit is the smallest unit of the temperature).
Therefore the formula used for the conversion of degree Celsius and Fahrenheit are:
  ⟹  \implies ∘F  =(∘C∗9/5)+32^\circ {\rm{F}}\;{\rm{ = (}}^\circ {\rm{C}} * 9/5) + 32
  ⟹  \implies ∘C  =(∘F−32)∗5/9^\circ {\rm{C}}\;{\rm{ = (}}^\circ {\rm{F - 32)}} * 5/9
By using the old algebra trick
  ⟹  \implies ∘F=∘C^\circ {\rm{F = }}^\circ {\rm{C }}
⇒∘C =(∘C∗9/5)+32\Rightarrow ^\circ {\rm{C}}\,{\rm{ = (}}^\circ {\rm{C }} * {\rm{ 9/5) + 32}}
⇒  ∘C −(∘C∗9/5)=32\Rightarrow \;^\circ {\rm{C}}\, - {\rm{ (}}^\circ {\rm{C }} * {\rm{ 9/5) = 32}}
 ⇒  5∘C−9∘C5  =  32\, \Rightarrow \;\dfrac{{5^\circ {\rm{C - 9}}^\circ {\rm{C}}}}{5}\; = \;32
⇒ −4/5  ∘C  =  3\Rightarrow \, - 4/5\;^\circ {\rm{C}}\;{\rm{ = }}\;{\rm{3}}
⇒  ∘C  =−32∗  5/4\Rightarrow \;^\circ {\rm{C}}\;{\rm{ = - 32}} * \;{\rm{5/4}}
⇒∘C=−40∘\Rightarrow {\rm{ }}^\circ {\rm{C = - 40}}^\circ
Now, ∘F =(∘F∗9/5)+32^\circ {\rm{F}}\,{\rm{ = (}}^\circ {\rm{F }} * {\rm{ 9/5) + 32}}
⇒  ∘F −(∘F∗9/5)=32\Rightarrow \;^\circ {\rm{F}}\, - {\rm{ (}}^\circ {\rm{F}} * {\rm{ 9/5) = 32}}
 ⇒  5∘F−9∘F5  =  32\, \Rightarrow \;\dfrac{{5^\circ {\rm{F - 9}}^\circ {\rm{F}}}}{5}\; = \;32
⇒ −4/5  ∘F  =  3\Rightarrow \, - 4/5\;^\circ {\rm{F}}\;{\rm{ = }}\;{\rm{3}}
⇒  ∘F=−32∗  5/4\Rightarrow \;^\circ {\rm{F = - 32}} * \;{\rm{5/4}}
⇒∘F=−40∘\Rightarrow ^\circ {\rm{F = - 40}}^\circ
Thus the temperature of both scales is the same as given above.
Hence the correct option is D.

Note: Both the scales Celsius and Fahrenheit have their thermometer for the measurements. Besides these two temperatures, two more types of temperature exist: the Kelvin scale and the Rankin scale. Moreover, from all the four temperatures, the Celsius and Fahrenheit scales are the most commonly used, whereas the Kelvin is used for scientific experiments.