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Question: The value of absolute zero temperature in Fahrenheit scale is : A. \( - {273^ \circ }F\) B. \(...

The value of absolute zero temperature in Fahrenheit scale is :
A. −273∘F - {273^ \circ }F
B. −32∘F - {32^ \circ }F
C. −460∘F - {460^ \circ }F
D. −132∘F - {132^ \circ }F

Explanation

Solution

When the temperature reaches zero on the Kelvin scale, it is termed as absolute zero. The conversion formula for converting Celsius to fahrenheit is –
∘F=95C+32^ \circ F = \dfrac{9}{5}C + 32

Complete step-by-step answer:
Historically, there have been many units along with scales to define temperature. Some of the famous ones are Celsius and Fahrenheit scales. Different units are used in different regions of the world, like Fahrenheit scale is used in the USA and Celsius scale is used in the rest of the world.
However, in scientific notations, the SI unit of temperature is Kelvin. The Kelvin scale has been accepted as the standard scale for temperature universally, for scientific notations.
One kelvin is defined as the change in the thermodynamic temperature T, that results in rise in the thermal energy by kTkT where kk is called the Boltzmann’s constant , which is equal to 1.38×10−23JK−11.38 \times {10^{ - 23}}J{K^{ - 1}}
The starting point of the Kelvin scale is called Absolute Zero or 0 K.
Absolute zero is defined as the lowest point in the thermodynamic temperature scale, a point at which the thermodynamic properties such as enthalpy and entropy of the ideal gases, reach the most minimum values. At this point, the molecules have no vibrational kinetic energy.
The absolute zero is referenced on a Celsius scale.
Absolute zero on the Celsius scale = −273∘C - {273^ \circ }C
By converting this to Fahrenheit, we have –
∘F=95C+32^ \circ F = \dfrac{9}{5}C + 32
Substituting the value of absolute zero, we have –
∘F=95C+32 ∘F=95×−273+32 Solving, ∘F=−24575+32 ∘F=−491.4+32 ∘F=−459.4≃−460∘  ^ \circ F = \dfrac{9}{5}C + 32 \\\ ^ \circ F = \dfrac{9}{5} \times - 273 + 32 \\\ Solving, \\\ ^ \circ F = - \dfrac{{2457}}{5} + 32 \\\ ^ \circ F = - 491.4 + 32 \\\ ^ \circ F = - 459.4 \simeq - {460^ \circ } \\\
The temperature of absolute zero in Fahrenheit scale is = −460∘F - {460^ \circ }F

Hence, the correct option is Option C.

Note: Sometimes, students can make a very simple mistake in converting Celsius to Fahrenheit. They will be confused with 95C+32\dfrac{9}{5}C + 32 and 95(C+32)\dfrac{9}{5}\left( {C + 32} \right).
To avoid that confusion, it is remembered that 0∘C=32∘F{0^ \circ }C = {32^ \circ }F. Substituting the value of 0∘C{0^ \circ }C in each of the equations, either one of them will yield the correct answer i.e. 32∘F{32^ \circ }F.
Similarly, to convert Fahrenheit to Celsius, it is 59(F−32)\dfrac{5}{9}\left( {F - 32} \right) and not 59F−32\dfrac{5}{9}F - 32. Here, substituting the value of 32∘F{32^ \circ }F, either one of them will give the correct value of 0∘C{0^ \circ }C