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Question: A temperature difference of \(30^\circ\) in the Fahrenheit scale is : A. \(54^\circ\) B. \(27^\c...

A temperature difference of 30∘30^\circ in the Fahrenheit scale is :
A. 54∘54^\circ
B. 27∘27^\circ
C. 86∘86^\circ
D. −54∘-54^\circ

Explanation

Solution

Temperature is a physical number that describes how hot or cold something is. When a body comes into contact with another that is colder or hotter, it is the manifestation of thermal energy, which is present in all matter and is the cause of the occurrence of heat, a flow of energy. The solution to the problem is based on this notion.

Complete step by step answer:
The degree Celsius is a temperature unit on the Celsius scale, which was previously known as the centigrade scale. The degree Celsius can refer to a specific temperature on the Celsius scale or a unit used to represent a temperature difference or range. It was named after Anders Celsius (1701–1744), a Swedish astronomer who devised a comparable temperature scale.

The Fahrenheit scale is a temperature scale based on Daniel Gabriel Fahrenheit (1686–1736), a scientist who established it in 1724. The temperature is measured in degrees Fahrenheit. There are several stories of how he created his scale in the beginning, but the original article says that the lowest defining point, 0 °F, was set as the freezing temperature of a brine solution formed from water, ice, and ammonium chloride (a salt).

The following is the relationship between the fahrenheit and celsius scales:
tC−0100=tF−32180\dfrac{{{t_C} - 0}}{{100}} = \dfrac{{{t_F} - 32}}{{180}}
Given, tC=30∘C{t_C} = {30^\circ }{\text{C}}.
Hence, 30−0100=tF−32180\dfrac{{30 - 0}}{{100}} = \dfrac{{{{\text{t}}_{\text{F}}} - 32}}{{180}}
⇒6=tF−329\Rightarrow 6 = {{\text{t}}_{\text{F}}} - \dfrac{{32}}{9}
⇒tF−32=54\Rightarrow {{\text{t}}_{\text{F}}} - 32 = 54
∴tF=32+54=86∘F\therefore {{\text{t}}_{\text{F}}} = 32 + 54 = {86^\circ }{\text{F}}

Hence, the correct answer is option C.

Note: Make sure you follow the correct unit conversions. The temperature at which pure water ice melts is now commonly defined as 32 °F, while the boiling point of water is now usually specified as 212 °F, both at sea level and at normal atmospheric pressure (a 180 °F difference).