An organic chemist measures the temperature [tex]$T$[/tex] of a solution in a reaction flask. Here is the result:
[tex]$T=21.3{ }^{\circ} C$[/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 the given temperature: T ( K ) = 21.3 + 273.15 = 294.45 .
Round the result to 4 significant figures: $294.45
The temperature in Kelvin is: 294.45
Explanation
Understanding the Problem We are given the temperature of a solution in Celsius, T = 21.3 ∘ 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 where T ( K ) is the temperature in Kelvin and T ( ∘ C ) is the temperature in Celsius.
Calculating Kelvin Temperature Now, we substitute the given temperature in Celsius into the formula: T ( K ) = 21.3 + 273.15 = 294.45 So, the temperature in Kelvin is 294.45 K.
Rounding to Significant Figures We are asked to round the answer to 4 significant figures. Since 294.45 already has 5 significant figures, we need to round it to 4. The first four digits are 294.4, and the next digit is 5, so we don't need to round up. Therefore, the rounded temperature in Kelvin is 294.4 K.
Final Answer Therefore, the temperature in SI units (Kelvin), rounded to 4 significant figures, is 294.45 K.
Examples
Temperature conversion is essential in many real-world applications. For instance, in cooking, a recipe might specify oven temperatures in Fahrenheit, but your oven displays Celsius. Converting between these units ensures you set the correct temperature for baking. Similarly, in scientific research, converting Celsius to Kelvin is crucial because many formulas and calculations require absolute temperature values. Accurate temperature measurements and conversions are also vital in weather forecasting, climate studies, and various engineering applications to maintain precision and consistency.
To convert the temperature from Celsius to Kelvin, the formula used is T ( K ) = T ( ° C ) + 273.15 . For the given temperature of 21.3 °C, after applying the formula, we get 294.45 K, which rounds to 294.4 K when expressed in 4 significant figures.
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