which of the following temperatures is the lowest? A.100CB.100FC.100K D. they are all the same

UpStudy Free Solution:

To determine which temperature is the lowest, we need to convert all the given temperatures to the same unit. Let's convert them all to degrees Celsius (\(^ \circ \text { C} \)):

1. \(100  ^ \circ \text { C} \) is already in Celsius.

2. \(100  ^ \circ \text { F} \) can be converted to Celsius using the formula:

\[T( ^ \circ \text { C} ) = \frac { 5} { 9} ( T( ^ \circ \text { F} ) - 32) \]

So,

\[100 ^ \circ \text { F} = \frac { 5} { 9} ( 100 - 32) = \frac { 5} { 9} \times 68 \approx 37.78 ^ \circ \text { C} \]

3. \(100 \space \text { K} \) can be converted to Celsius using the formula:

\[T( ^ \circ \text { C} ) = T( \text { K} ) - 273.15\]

So,

\[100  \text { K} = 100 - 273.15 = - 173.15  ^ \circ \text { C} \]

Now we have the temperatures in Celsius:

- \(100  ^ \circ \text { C} \)

- \(37.78  ^ \circ \text { C} \)

- \(- 173.15 ^ \circ \text { C} \)

Clearly, \(- 173.15  ^ \circ \text { C} \) is the lowest temperature.

Therefore, the correct answer is:

C. \(100 \space \text { K} \)

Supplemental Knowledge

Understanding temperature conversion is essential in various scientific fields, including physics and chemistry. Here’s a deeper dive into the topic:

- Temperature Scales:

- Celsius (\(^ \circ \text { C} \)): A scale where water freezes at \(0^ \circ \text { C} \) and boils at \(100^ \circ \text { C} \) under standard atmospheric conditions.

- Fahrenheit (\(^ \circ \text { F} \)): A scale where water freezes at \(32^ \circ \text { F} \) and boils at \(212^ \circ \text { F} \).

- Kelvin (K): An absolute temperature scale starting from absolute zero, the theoretical point where all molecular motion stops. Water freezes at \(273.15 \space \text { K} \) and boils at \(373.15 \space \text { K} \).

- Conversion Formulas:

- From Fahrenheit to Celsius:

\[T( ^ \circ \text { C} ) = \frac { 5} { 9} ( T( ^ \circ \text { F} ) - 32) \]

- From Kelvin to Celsius:

\[T( ^ \circ \text { C} ) = T( \text { K} ) - 273.15\]

- Example Calculations:

- Converting \(100^ \circ \) Fahrenheit to Celsius:

\[T( ^ \circ \text { C} ) = \frac { 5} { 9} ( 100 - 32) = 37.78^ \circ \text { C} \]

- Converting \(100\space K\) to Celsius:

\[T( ^ \circ \text { C} ) = 100\space K - 273.15 = - 173.15^ \circ \text { C} \]

These conversions help in comparing temperatures across different scales accurately.

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