Question

Convert the following temperatures to kelvins. a. \(0^{\circ} \mathrm{C}\) b. \(25^{\circ} \mathrm{C}\) c. \(37^{\circ} \mathrm{C}\) d. \(100^{\circ} \mathrm{C}\) e. \(-175^{\circ} \mathrm{C}\) f. \(212^{\circ} \mathrm{C}\)

Short answer

The converted temperatures in Kelvin are: a. 273.15 K b. 298.15 K c. 310.15 K d. 373.15 K e. 98.15 K f. 485.15 K

Step-by-step solution

Conversion Formula

To convert the temperatures from Celsius to Kelvin, we'll use the equation K = C + 273.15. a. \(0^{\circ} \mathrm{C}\)

Convert 0°C to Kelvin

Using the temperature conversion formula, we have: K = 0 + 273.15 = 273.15 K. b. \(25^{\circ} \mathrm{C}\)

Convert 25°C to Kelvin

Using the temperature conversion formula, we have: K = 25 + 273.15 = 298.15 K. c. \(37^{\circ} \mathrm{C}\)

Convert 37°C to Kelvin

Using the temperature conversion formula, we have: K = 37 + 273.15 = 310.15 K. d. \(100^{\circ} \mathrm{C}\)

Convert 100°C to Kelvin

Using the temperature conversion formula, we have: K = 100 + 273.15 = 373.15 K. e. \(-175^{\circ} \mathrm{C}\)

Convert -175°C to Kelvin

Using the temperature conversion formula, we have: K = -175 + 273.15 = 98.15 K. f. \(212^{\circ} \mathrm{C}\)

Convert 212°C to Kelvin

Using the temperature conversion formula, we have: K = 212 + 273.15 = 485.15 K.

Key concepts

Celsius to Kelvin

Understanding the relationship between Celsius and Kelvin scales is crucial for students studying science and thermodynamics. These temperature scales are used in different contexts, with Celsius being common for everyday temperature measurements and Kelvin used extensively in scientific research. The Kelvin scale starts at absolute zero, the theoretical point where particles have minimal thermal motion. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature, reflecting the difference in starting points.

For instance, when converting room temperature, typically about 25°C, to Kelvin, we simply perform the following operation: \( K = 25 + 273.15 = 298.15 \). This straightforward addition ensures measurements are more compatible with scientific equations that use Kelvin, like those related to ideal gas laws or the behavior of blackbody radiators.

Temperature Conversion Formula

The temperature conversion formula is indispensable for students to translate measurements from one temperature scale to another. For converting Celsius to Kelvin, the formula is quite simple: \( K = C + 273.15 \), where \(K\) represents the temperature in Kelvin and \(C\) stands for the temperature in Celsius. Memorizing this formula is immensely beneficial, as it quickly allows students to switch between scales without needing a calculator or conversion chart. This equation signifies more than just a method for conversion—it symbolizes the relation between the scales, highlighting that Kelvin is an extension of the Celsius scale offset by 273.15.

Kelvin Scale

The Kelvin scale is a thermodynamic temperature scale named after William Thomson, 1st Baron Kelvin, who first proposed it in 1848. It's an absolute scale, meaning it starts from absolute zero, the point at which no more thermal energy can be removed from a system.

Unlike Celsius or Fahrenheit, the Kelvin scale does not use degrees. Instead, it's simply referred to by the unit 'Kelvin' (symbolized as K). This distinction emphasizes the absolute nature of the scale. In Kelvin, 0 K is absolute zero, and because of this, temperatures in Kelvin can never be negative.

The Kelvin scale sees wide-ranging use in scientific disciplines such as physics and chemistry, where precise temperature measurements are fundamental.

Thermodynamic Temperature

Thermodynamic temperature is a measure of the absolute temperature of an object, defined in terms of its ability to give off or absorb energy in the form of heat. Its unit is the Kelvin, and it reflects the kinetic energy of the particles that make up the material.

Thermodynamic temperature is different from the temperature measured by a thermometer, which is often a relative measure compared to a reference point, like the freezing or boiling point of water. Understanding thermodynamic temperature is vital for interpreting the behavior of gases, calculating the efficiency of heat engines, and it's the cornerstone of laws in thermodynamics, such as entropy and the second law of thermodynamics.