Question

The temperature of liquid hydrogen is 20 K. What is this temperature on the Fahrenheit scale?

$
  A{.495.4^0}F \\
  B. - {423.4^0}F \\
  C. - {108.56^0}F \\
  D. - {487.4^0}F \\
 $

Answer 1

Hint: In the question, we need to determine the equivalent temperature value of 20 Kelvin on the Fahrenheit scale. For this, we will use the formula $F = \dfrac{9}{5}\left( {K - 273} \right) + 32$ for the conversion of Fahrenheit to Kelvin and vice versa where F is the absolute value of the temperature in the Fahrenheit scale and K is the absolute value of the temperature in the Kelvin scale.

Complete step by step answer:

The temperature of an object can be measured in different units. Kelvin is the SI unit of the temperature. It is denoted by the letter “K”. Initially, all the measurement and calculations were made on the degree Celsius only, but when the Fahrenheit has been universally accepted as one of the units of temperature, there established a relation between degree Fahrenheit and the Kelvin as $F = \dfrac{9}{5}\left( {K - 273} \right) + 32$.

Now, substituting the value 20 Kelvin in the formula $F = \dfrac{9}{5}\left( {K - 273} \right) + 32$ to determine the equivalent temperature in Fahrenheit scale as:

$
  F = \dfrac{9}{5}\left( {K - 273} \right) + 32 \\
   = \dfrac{9}{5}\left( {20 - 273} \right) + 32 \\
   = \dfrac{9}{5}\left( { - 253} \right) + 32 \\
   = \dfrac{{ - 2277}}{5} + 32 \\
   = - 455.4 + 32 \\
   = - 423.4{\text{ }}{}^0F \\
 $

Hence, we can say that the temperature of liquid hydrogen is 20 K. What is this temperature on the Fahrenheit scale is -423.4 degree Fahrenheit.

So, the correct answer is “Option B”.

Note:
Students should not get confused with the terms $20K$ and $ - 423.4{}^0F$. These two terms are similar and are written in two different forms only as the temperature of the liquid hydrogen is $20K$ which is similar to $ - 423.4{}^0F$ in Fahrenheit Scale. Moreover, the sign the values of the temperature should be kept with the sign convention as well.