Problem 25 - Introductory Chemistry Atoms First

Question

How do you convert from \({ }^{\circ} \mathrm{C}\) to \(\mathrm{K}\) ? Convert room temperature \(\left(22.0^{\circ} \mathrm{C}\right)\) to Kelvin.

Step-by-Step Solution

Answer

To convert a temperature in Celsius (°C) to Kelvin (K), add 273.15 to the Celsius temperature. Given room temperature is 22.0°C. Thus, the temperature in Kelvin is 22.0°C + 273.15 = \(295.15\, K\).

Step 1: Understanding the relationship between Celsius and Kelvin

The Celsius and Kelvin temperature scales have a simple linear relationship. To convert a temperature in Celsius (°C) to Kelvin (K), we add 273.15 to the Celsius temperature: Temperature in Kelvin (K) = Temperature in Celsius (°C) + 273.15

Step 2: Identify the room temperature in Celsius

The given room temperature is 22.0°C.

Step 3: Convert room temperature to Kelvin

Now, we will use the relationship in step 1 to convert the room temperature from Celsius to Kelvin. Temperature in Kelvin (K) = 22.0°C + 273.15 Temperature in Kelvin (K) = \(295.15\)

Step 4: Write the final answer

The room temperature in Kelvin is \(295.15\, K\).

Key Concepts

Temperature Scales

Temperature measures the degree of heat or coldness of an object and is a fundamental aspect of our daily lives, science, and technology. It tells us about the kinetic energy of the particles in a substance, which becomes greater as the temperature increases. There are several ways to measure temperature, and these are encapsulated in different temperature scales.

Two of the most widely used temperature scales are Celsius and Kelvin. The Celsius scale, denoted by °C, is used for everyday temperature measurements in most countries around the world. It defines the melting point of ice as 0°C and the boiling point of water at standard atmospheric pressure as 100°C. The Kelvin scale, denoted by K, is the base unit of temperature in the International System of Units (SI) and is widely used in the science and engineering fields. Unlike Celsius, which can have negative values, the Kelvin scale is an absolute temperature scale with its zero point set at absolute zero, the theoretical point at which particles have minimal thermal motion. In the conversion process, understanding these scales and their starting points is essential.

For all practical purposes, the temperature intervals are the same for Celsius and Kelvin, meaning that a change of one degree Celsius is equivalent to a change of one Kelvin. This simplicity in relation is what makes converting between these two scales straightforward.

Kelvin Temperature Scale

The Kelvin temperature scale is named after the British physicist and engineer William Thomson, also known as Lord Kelvin. It is an absolute thermodynamic temperature scale that begins at absolute zero. Absolute zero (\(0\text{ K}\)) is the temperature at which all thermal motion in matter ceases and is considered the lowest limit of the thermodynamic temperature scale.

Unlike the Celsius scale, where temperature can be negative, the Kelvin scale only deals with positive values, making it particularly useful for scientific and technical fields where negative temperatures can cause confusion. For this reason, Kelvin is the unit of temperature measurement for expressing scientific temperatures, such as in the study of thermodynamics, physics, and chemistry.

Another key aspect of the Kelvin scale that is important for converting temperatures is that it uses the same incremental value as Celsius. This means that a temperature change of one Kelvin is the same magnitude as that of one degree Celsius. Therefore, there is no conversion factor for the magnitude of temperature changes - just a shift in the starting point.

Celsius Temperature Scale

The Celsius temperature scale, formerly known as the centigrade scale, is familiar to most due to its widespread use in daily life, from weather forecasts to cooking. Developed by Anders Celsius, it is a convenient scale for practical purposes because of its definition based on the freezing and boiling points of water.

In the Celsius scale, the space between these points is divided into 100 equal parts, each representing one degree of temperature change. This makes the scale intuitive to use for people and allows for easy communication of weather-related temperatures or the comparison of temperatures in a common context like home and work environments.

When converting Celsius to other scales like Kelvin, it's useful to remember that water freezes at 0°C and boils at 100°C at sea-level atmospheric pressure, while the corresponding values in Kelvin are approximately 273.15 K and 373.15 K, respectively. The fixed point of 0 K in Celsius is \( -273.15^\circ\text{C} \), establishing the pivotal difference that must be added or subtracted when converting between these scales. In practical use, to convert Celsius to Kelvin, we add 273.15 to the Celsius temperature, signifying the offset without altering the size of the unit increment.