Ch.1 - Chemical Tools: Experimentation & Measurement

Problem 5c

Chapter 1, Problem 5c

The temperature on the surface of the Sun is 5778 K. What is the temperature in degrees Fahrenheit? (LO 1.6) (c) 10,920 °F

Verified step by step guidance

Start with the formula to convert Kelvin to Celsius: \( T_{\text{C}} = T_{\text{K}} - 273.15 \).

Substitute the given temperature in Kelvin (5778 K) into the formula to find the temperature in Celsius.

Use the formula to convert Celsius to Fahrenheit: \( T_{\text{F}} = \frac{9}{5}T_{\text{C}} + 32 \).

Substitute the calculated Celsius temperature into the formula to find the temperature in Fahrenheit.

Perform the arithmetic operations to complete the conversion from Celsius to Fahrenheit.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Temperature Scales

Temperature can be measured in different scales, primarily Celsius, Kelvin, and Fahrenheit. The Kelvin scale is an absolute temperature scale used in scientific contexts, where 0 K represents absolute zero. The Fahrenheit scale is commonly used in the United States, where water freezes at 32 °F and boils at 212 °F. Understanding how to convert between these scales is essential for solving temperature-related problems.

Conversion Formulas

To convert temperatures between Kelvin and Fahrenheit, specific formulas are used. The conversion from Kelvin (K) to Fahrenheit (°F) is given by the formula °F = (K - 273.15) × 9/5 + 32. This formula accounts for the differences in the zero points and scaling factors of the two temperature systems, allowing for accurate temperature conversion.

Scientific Notation and Significant Figures

In scientific contexts, it is important to express numbers in a way that reflects their precision. Significant figures indicate the certainty of a measurement, while scientific notation allows for the representation of very large or small numbers in a compact form. When performing calculations, especially conversions, maintaining the correct number of significant figures ensures that the final answer is both accurate and meaningful.

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