Understanding Kelvin and Celsius Temperature Scales

The question asks for the correct relationship between the Kelvin temperature, denoted by \(T\), and the Celsius temperature, denoted by \(t_c\). Both are scales used to measure temperature, but they have different reference points.

Kelvin and Celsius Scales Overview

• Celsius Scale (\(t_c\)): This scale is widely used globally. Its reference points are the freezing point of water defined as 0°C and the boiling point of water defined as 100°C under standard atmospheric pressure.
• Kelvin Scale (\(T\)): This is the SI base unit for temperature and is an absolute thermodynamic scale. Its zero point, 0 K, is defined as absolute zero, the theoretical point where particle motion ceases, which is approximately -273.15°C. The size of one Kelvin degree is equal to the size of one Celsius degree.

Establishing the Relationship

Since the size of a degree is the same on both scales, the conversion between them is a simple shift based on the difference between their zero points. The zero point of the Kelvin scale (0 K) corresponds to -273.15°C on the Celsius scale.

Therefore, to convert a temperature from Celsius (\(t_c\)) to Kelvin (\(T\)), you need to add the value of the Kelvin zero point in Celsius (273.15) to the Celsius temperature.

The formula for converting Celsius temperature (\(t_c\)) to Kelvin temperature (\(T\)) is:

\[ T = t_c + 273.15 \]

Let's examine the given options based on this understanding.

Analyzing the Options

We will analyze each option provided in the question to determine which one represents the correct relationship between Kelvin temperature (\(T\)) and Celsius temperature (\(t_c\)).

1. Option 1: These are two independent temperature scales

   While Kelvin and Celsius are distinct scales, they are not independent. There is a precise mathematical relationship between them, allowing for conversion from one to the other. This statement is therefore incorrect in the context of finding a mathematical relation.

2. Option 2: \(T = t_c\)

   This option suggests that the Kelvin temperature is always equal to the Celsius temperature. This is incorrect because the scales have different zero points. For example, 0°C is 273.15 K, not 0 K.

3. Option 3: \(T = (t_c - 273.15)\)

   This formula represents the conversion from Kelvin to Celsius (\(t_c = T - 273.15\)). If you want to find \(t_c\) given \(T\), you would subtract 273.15. However, the question asks for \(T\) in terms of \(t_c\). This option is incorrect for converting \(t_c\) to \(T\).

4. Option 4: \(T = (t_c + 273.15)\)

   This option presents the formula \(T = t_c + 273.15\). This aligns exactly with the established relationship for converting Celsius temperature (\(t_c\)) to Kelvin temperature (\(T\)). Adding 273.15 to the Celsius temperature shifts the zero point correctly to align with the Kelvin scale.

Conclusion on the Temperature Relationship

Based on the analysis of the relationship between the Kelvin and Celsius scales and evaluating the options, the correct formula for converting Celsius temperature (\(t_c\)) to Kelvin temperature (\(T\)) is \(T = t_c + 273.15\).

Revision Table: Temperature Conversion Formulas

Additional Information on Temperature Scales

Understanding the relationship between temperature scales is fundamental in physics and various scientific applications. Here are a few more key points:

• Absolute Zero: The theoretical lowest possible temperature is 0 K, which corresponds to -273.15°C and -459.67°F. At absolute zero, the particles of matter would have minimal vibrational motion.
• Reference Points:
  • Freezing point of water: 0°C = 273.15 K = 32°F
  • Boiling point of water: 100°C = 373.15 K = 212°F
• Why 273.15? The value 273.15 comes from the definition of the Kelvin scale based on the triple point of water (the temperature and pressure at which water, ice, and water vapor coexist in equilibrium), which is defined as 273.16 K. The zero point of Celsius is set at the freezing point of water (0.00 °C), which was experimentally determined to be 273.15 K above absolute zero.
• Temperature vs. Heat: Temperature is a measure of the average kinetic energy of the particles within a system, while heat is the transfer of thermal energy between systems due to a temperature difference.

Mastering these conversions and concepts is important for solving problems involving heat, thermodynamics, and various physical sciences.