Question

Convert the following temperatures to kelvin: (a) \(115.21^{\circ} \mathrm{C},\) the melting point of sulfur; (b) \(37^{\circ} \mathrm{C}\), the normal body temperature; (c) \(357^{\circ} \mathrm{C},\) the boiling point of mercury.

Short answer

115.21°C is 388.36 K, 37°C is 310.15 K, and 357°C is 630.15 K.

Step-by-step solution

Understanding Temperature Conversion

To convert temperatures from Celsius to Kelvin, we use the formula: \[ K = {}^{ ext{C}} ext{Celsius} + 273.15 \] This formula accounts for the fact that the Kelvin scale and the Celsius scale are offset by 273.15 degrees.

Convert 115.21°C to Kelvin

Use the conversion formula to convert 115.21°C to Kelvin:\[ K = 115.21 + 273.15 \]Calculate this to get:\[ K = 388.36 \]Therefore, 115.21°C is equivalent to 388.36 K.

Convert 37°C to Kelvin

Use the conversion formula to convert 37°C to Kelvin:\[ K = 37 + 273.15 \]Calculate this to get:\[ K = 310.15 \]Thus, 37°C is equivalent to 310.15 K.

Convert 357°C to Kelvin

Use the conversion formula to convert 357°C to Kelvin:\[ K = 357 + 273.15 \]Calculate this to get:\[ K = 630.15 \]Consequently, 357°C is equivalent to 630.15 K.

Key concepts

Celsius to Kelvin conversion

Temperature conversion is a common task, especially when working in scientific contexts. Converting from Celsius to Kelvin is straightforward due to their simple relationship. The key formula is:\[ K = °C + 273.15 \]This formula reflects that the Kelvin scale is simply offset from the Celsius scale by 273.15 units. Kelvin is the SI unit for temperature, often used in scientific calculations, while Celsius is more common in everyday situations. By adding 273.15 to a Celsius temperature, you shift the starting point of the scale from the freezing point of water (0°C) to absolute zero (0 K). This conversion is necessary when using equations that require absolute temperature values to avoid negative numbers and ensure accuracy.

Kelvin scale

The Kelvin scale is a thermodynamic temperature scale used widely in science and engineering. Unlike Celsius or Fahrenheit, the Kelvin scale does not use degrees. Instead, it measures temperature in absolute terms, meaning its zero point, called absolute zero, is the lowest theoretical temperature possible.

• Absolute zero is 0 K, equivalent to -273.15°C, where molecular motion theoretically stops.
• Kelvin is favored in scientific settings because it directly relates to energy measurements in physics and chemistry.
• It helps avoid negative numbers in thermodynamic calculations, which simplifies the math.

Understanding the Kelvin scale is essential for studying physical phenomena under extreme conditions or when precision is critical.

Melting point of sulfur

Sulfur is a chemical element with a distinct melting point, which indicates the temperature at which it transitions from solid to liquid. This temperature is a fixed physical property of the element, used to identify substances and determine purity. The melting point of sulfur is 115.21°C.In Kelvin, this is: \[ K = 115.21 + 273.15 = 388.36 K \]Sulfur's melting point is significant in geological and industrial processes. It is often involved in volcanic activities and is also used in the manufacture of products like sulfuric acid. Knowing its precise melting point aids in these processes, integrating its conversion into Kelvin ensures calculation consistency in experiments.

Boiling point of mercury

Mercury is unique as a liquid metal, and its boiling point is crucial for applications requiring precise temperature management. The boiling point of mercury is 357°C.Converted to Kelvin:\[ K = 357 + 273.15 = 630.15 K \]

• Mercury is used in barometers, thermometers, and other scientific instruments.
• Its boiling point is high, making it useful for measuring temperatures in extreme conditions.
• Understanding mercury's boiling point is important in safety, as mercury can be toxic when vaporized.

Converting to Kelvin ensures precision and consistency in calculations that involve high temperatures, which is particularly essential in thermodynamic studies.

Normal body temperature

Normal body temperature is a physiological baseline used to assess health. On average, it is around 37°C, though slight variations can occur between individuals and throughout the day. In scientific contexts, understanding and converting this temperature to Kelvin can be useful, particularly in medical research or in developing temperature-sensitive equipment.In Kelvin, normal body temperature converts to:\[ K = 37 + 273.15 = 310.15 K \]

• A consistent temperature is crucial for maintaining metabolic processes.
• Deviations might indicate illness or other health conditions.
• Converting to Kelvin helps in scientific measurements associated with body temperature.

Recognizing these temperature conversions can enhance understanding in medical studies and in improving patient care technologies.