A physical chemist measures the temperature [tex]$T$[/tex] inside a vacuum chamber. Here is the result:
[tex]$T=-70.941{ }^{\circ} C$[/tex]
Convert [tex]$T$[/tex] to SI units. Round your answer to 6 significant figures.
______ K ______ [tex]$\times 10$[/tex]
Answer (1)
Convert Celsius to Kelvin using the formula: T ( K ) = T ( ∘ C ) + 273.15 .
Substitute the given temperature: T ( K ) = − 70.941 + 273.15 .
Calculate the temperature in Kelvin: T ( K ) = 202.209 .
The temperature in Kelvin, rounded to 6 significant figures, is 202.209 .
Explanation
Understanding the Problem We are given the temperature in Celsius, T = − 70.941 ∘ C , and we need to convert it to Kelvin (K), which is the SI unit for temperature.
Conversion Formula To convert Celsius to Kelvin, we use the formula: T ( K ) = T ( ∘ C ) + 273.15
Substitution Substitute the given temperature in Celsius into the formula: T ( K ) = − 70.941 + 273.15
Calculation Calculate the temperature in Kelvin: T ( K ) = 202.209
Rounding and Final Answer Round the result to 6 significant figures. Since the result is already given to 6 significant figures, we don't need to round it further. Therefore, the temperature in Kelvin is 202.209 K .
Examples
Converting temperatures between Celsius and Kelvin is essential in many scientific and engineering applications. For example, when studying the behavior of gases, the ideal gas law, P V = n RT , requires the temperature to be in Kelvin. Similarly, in thermodynamics, calculations involving energy changes often require temperatures in Kelvin to ensure consistency with other SI units. Understanding temperature conversions helps in accurately modeling and predicting the behavior of systems in various fields.
