A physical chemist measures the temperature [tex]$T$[/tex] inside a vacuum chamber. Here is the result:
[tex]$T=-13.8^{\circ} C$[/tex]
Convert [tex]$T$[/tex] to SI units. Round your answer to 4 significant figures.
Answer (2)
Convert Celsius to Kelvin using the formula: T ( K ) = T ( ∘ C ) + 273.15 .
Substitute T ( ∘ C ) = − 13.8 into the formula: T ( K ) = − 13.8 + 273.15 .
Calculate T ( K ) = 259.35 .
Round to 4 significant figures: T ( K ) = 259.4 .
Explanation
Understanding the Problem We are given the temperature in Celsius, T = − 13. 8 ∘ C , and we need to convert it to Kelvin (K), which is the SI unit for temperature. We need to round the answer to 4 significant figures.
Conversion Formula To convert Celsius to Kelvin, we use the formula: T ( K ) = T ( ∘ C ) + 273.15
Substitution Substitute the given temperature T = − 13. 8 ∘ C into the formula: T ( K ) = − 13.8 + 273.15
Calculation Calculate the value of T ( K ) :
T ( K ) = 259.35
Rounding Round the result to 4 significant figures. Since the result is already given to 5 significant figures, we round it to 4 significant figures: T ( K ) = 259.4
Final Answer Therefore, the temperature in Kelvin is 259.4 K.
Examples
Converting temperature from Celsius to 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 for accurate calculations. Similarly, in thermodynamics, many equations involve temperature, and using Kelvin ensures consistency with other SI units. In everyday life, understanding temperature conversions helps in interpreting weather reports or setting thermostats accurately.
The temperature of -13.8°C converts to 259.4 K using the formula T ( K ) = T ( ∘ C ) + 273.15 . After calculating, we round the result to 4 significant figures. Therefore, the final answer is 259.4 K.
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