Question

Which unit of the following is smaller?a.)one kelvinb.)one degree Celsius c.)one degree Fahrenheit

Answer 1

c) one degree Farenheit

Step-by-step explanation

to solve this let's convert 1° C into kelvin and Celsiuts, then,let's compare

Step 1

a) convert 1 °C into Kelvin:

to do that, we need to use the formula

`\begin{gathered} °K=C+237\text{ \degree} \\ replace \\ °K=1\text{ +237\degree} \\ °K=238°\text{ K} \end{gathered}`

hence

`1\text{ \degree C=238 K}`

so, one degree Kelvin is smaller than aone degree celsius ( note that 1° C= 238 °K)

Step 2

now, let's convert 1° C into Farenheit

we need to use the formula:

`\begin{gathered} °F=1.8\text{ C+32} \\ where\text{ C is the measure in \degree C} \end{gathered}`

replace and calculate

`\begin{gathered} \begin{equation*} °F=1.8\text{ C+32} \end{equation*} \\ °F=(1.8*1)+32=33.8 \\ °F=33.8\text{ \degree F} \end{gathered}`

so

`1\text{ \degree C=38.3 \degree F}`

so, one degree Fahrenheit is smaller than aone degree celsius ( note that 1° C= 38.3 °F)

Step 3

finally, compare °F and °K

`\begin{gathered} 1\text{ \degree C=238 \degree K=38.3 \degree F} \\ 238°K=38.3°F \\ F=(238)/(38.3)K \\ F=6.21\text{ \degree K} \end{gathered}`

so, the measure in °F is six times the measure in °K

therefore,

the smaller unit is

c) one degree Fahrenheit

I hope this helps you