Question

Perform the following conversions. a) \(100.0^{\circ} \mathrm{C}\) to kelvins b) \(-100.0^{\circ} \mathrm{C}\) to kelvins c) \(100 \mathrm{~K}\) to degrees Celsius d) \(300 \mathrm{~K}\) to degrees Celsius

Short answer

a) 373.15 K; b) 173.15 K; c) -173.15°C; d) 26.85°C.

Step-by-step solution

Understanding the Conversion Formula

To convert temperatures between Celsius and Kelvin, we use the formula: \[ K = ^\circ C + 273.15 \] where \( K \) is the temperature in kelvins, and \( ^\circ C \) is the temperature in degrees Celsius.

Convert 100.0°C to Kelvin

Applying the formula: \[ 100.0^{\circ} \mathrm{C} + 273.15 = 373.15 \mathrm{~K} \] Thus, \( 100.0^{\circ} \mathrm{C} \) is equal to \( 373.15 \mathrm{~K} \).

Convert -100.0°C to Kelvin

Using the conversion formula: \[ -100.0^{\circ} \mathrm{C} + 273.15 = 173.15 \mathrm{~K} \] Therefore, \( -100.0^{\circ} \mathrm{C} \) is \( 173.15 \mathrm{~K} \).

Convert 100 K to Celsius

For Kelvin to Celsius conversion, rearrange the formula to: \[ ^\circ C = K - 273.15 \] Applying it to 100 K: \[ 100 \mathrm{~K} - 273.15 = -173.15^{\circ} \mathrm{C} \] So, \( 100 \mathrm{~K} \) equals \( -173.15^{\circ} \mathrm{C} \).

Convert 300 K to Celsius

Using the rearranged formula for 300 K: \[ 300 \mathrm{~K} - 273.15 = 26.85^{\circ} \mathrm{C} \] Therefore, \( 300 \mathrm{~K} \) is \( 26.85^{\circ} \mathrm{C} \).

Key concepts

Celsius to Kelvin conversion

Converting Celsius to Kelvin is a straightforward process, essential for students exploring scientific and thermodynamic concepts. The Kelvin scale is an absolute temperature scale starting from absolute zero. This means that unlike Celsius, which can have positive or negative values, Kelvin only has non-negative numbers. To convert a temperature from Celsius to Kelvin, you simply add 273.15. This number is derived from the zero point of the Kelvin scale, which is 273.15 units below the zero of the Celsius scale. This dependable conversion formula looks like this:

\[ K = ^\circ C + 273.15 \]

Some key points include:

• Kelvin is primarily used in scientific contexts where temperature measurements cannot fall below zero.
• When solving practical problems such as converting 100.0°C to Kelvin, you get 373.15 K.
• The conversion helps scientists and students ensure temperature comparisons are meaningful in experiments and research.

Kelvin to Celsius conversion

Converting Kelvin back to Celsius is equally simple and mirrors the logic of the initial conversion. The Kelvin scale's advantage is its non-negative numbers, useful across processes needing precision, as in physical sciences. To convert a temperature from Kelvin to Celsius, you subtract 273.15 from the Kelvin measurement. This subtraction reverses the initial addition when converting from Celsius to Kelvin. The formula generally applied is:

\[ ^\circ C = K - 273.15 \]

Here are some practical insights:

• Always subtract exactly 273.15 from the Kelvin value to switch back to degrees Celsius correctly.
• For instance, converting 300 K gives 26.85°C, making it simple to contextualize physical scenarios or experiments.
• This conversion is frequent in climate science and materials studies, among other fields.

Thermodynamic temperature scale

The thermodynamic temperature scale, on which the Kelvin scale is based, represents an essential development in understanding temperature. Unlike Celsius or Fahrenheit, Kelvin is not just another means of measuring temperature; it provides vital insights into the behavior of physical systems. Designed to facilitate deeper scientific work, this scale allows measurements starting from absolute zero, the coldest possible temperature where particles cease to move.

Important aspects of the thermodynamic temperature scale include:

• Absolute zero is a key concept at 0 K that helps circumscribe temperature limits in physical profession discussions.
• The Kelvin scale is used extensively across research sectors, helping identify phase changes, state transitions, and other critical scientific phenomena.
• It reinforces maths and physics curricula by providing a clear and practical tool that grounds abstract scientific paradigms in measurable reality.

Understanding these conversions and the scale's significance enhances comprehension of temperature-related phenomena and supports accurate scientific communication and education.