Ch.1 - Matter, Measurement & Problem Solving

Problem 53

Chapter 1, Problem 53

Convert each temperature. a. 32 °F to °C (temperature at which water freezes) b. 77 K to °F (temperature of liquid nitrogen) c. -109 °F to °C (temperature of dry ice) d. 98.6 °F to K (body temperature)

Verified step by step guidance

To convert from Fahrenheit (°F) to Celsius (°C), use the formula: \( °C = \frac{5}{9} (°F - 32) \).

To convert from Kelvin (K) to Fahrenheit (°F), first convert Kelvin to Celsius using \( °C = K - 273.15 \), then convert Celsius to Fahrenheit using \( °F = \frac{9}{5} °C + 32 \).

To convert from Fahrenheit (°F) to Celsius (°C), use the formula: \( °C = \frac{5}{9} (°F - 32) \).

To convert from Fahrenheit (°F) to Kelvin (K), first convert Fahrenheit to Celsius using \( °C = \frac{5}{9} (°F - 32) \), then convert Celsius to Kelvin using \( K = °C + 273.15 \).

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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 using different scales, primarily Celsius (°C), Fahrenheit (°F), and Kelvin (K). Each scale has its own zero point and degree increments. For example, 0 °C is the freezing point of water, while 32 °F is equivalent to 0 °C. Understanding these scales is essential for converting temperatures accurately.

Conversion Formulas

To convert temperatures between different scales, specific formulas are used. For instance, to convert Fahrenheit to Celsius, the formula is °C = (°F - 32) × 5/9. Similarly, to convert Kelvin to Celsius, the formula is °C = K - 273.15. Mastery of these formulas is crucial for solving temperature conversion problems.

Absolute Zero and Temperature Relationships

Kelvin is an absolute temperature scale where 0 K represents absolute zero, the theoretical point where molecular motion ceases. The relationship between Kelvin and Celsius is linear, with 0 °C equal to 273.15 K. Understanding this relationship is important for converting temperatures involving Kelvin, especially in scientific contexts.

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