Physics and Mathematics
Kelvin Scale of Temperature or Absolute Scale of Temperature
1. Concept Overview
The Kelvin Scale of Temperature (also called the Absolute Scale of Temperature) is a thermodynamic temperature scale based on the concept of absolute zero — the temperature at which the kinetic energy of all molecules becomes minimum (theoretically zero).
This scale provides a scientific and absolute reference for measuring temperature, unlike Celsius or Fahrenheit, which are based on arbitrary fixed points like the freezing and boiling points of water.
2. Explanation and Mathematical Derivation
In classical thermodynamics, temperature is directly related to the average kinetic energy of molecules.
At absolute zero (0 K), the molecular motion theoretically ceases:
[
E_k = 0
]
The Kelvin scale starts from this absolute zero.
The relationship between the Celsius scale and the Kelvin scale is given by:
[[T(K)] = [T(°C)] + [273.15]
That is,
- 0 °C = 273.15 K
- 100 °C = 373.15 K
This relation comes from the observation that equal temperature intervals on the Celsius and Kelvin scales are identical.
So, a change of 1 °C = a change of 1 K.
3. Dimensions and Units
| Quantity | Symbol | SI Unit | Dimensions |
|---|---|---|---|
| Temperature | [T] | Kelvin (K) | [Θ] |
4. Key Features
- Absolute zero (0 K) is the lowest possible temperature, where molecular motion stops.
- There are no negative temperatures on the Kelvin scale.
- 1 K increment equals 1 °C increment.
- Kelvin scale is based on fundamental physical properties rather than water-based reference points.
- It is the SI standard unit of temperature used in all thermodynamic equations.
- The Kelvin scale provides direct proportionality between temperature and average molecular kinetic energy.
5. Important Formulas to Remember
| Formula | Description |
|---|---|
| [T(K)] = [T(°C)] + [273.15] | Conversion from Celsius to Kelvin |
| [T(°C)] = [T(K)] – [273.15] | Conversion from Kelvin to Celsius |
| [E_k] ∝ [T(K)] | Average kinetic energy of molecules is proportional to absolute temperature |
6. Conceptual Questions with Solutions
1. What is meant by absolute zero?
Absolute zero is the temperature (0 K) at which the average kinetic energy of all molecules becomes minimum or theoretically zero.
2. Why is Kelvin scale called the absolute scale?
Because it starts from absolute zero, representing the true zero of temperature where molecular motion ceases completely.
3. Can the Kelvin temperature ever be negative?
No, because temperature in Kelvin measures absolute molecular energy, which cannot be less than zero.
4. How does 0 °C relate to Kelvin temperature?
0 °C corresponds to 273.15 K.
5. If a gas has a temperature of 300 K, what is it in Celsius?
[T(°C)] = [T(K)] – [273.15] = [300 – 273.15] = [26.85 °C]
6. Why is the Kelvin scale more suitable for scientific work?
Because it is based on absolute molecular energy and avoids negative values, simplifying thermodynamic calculations.
7. What does a temperature difference of 1 K represent?
A temperature difference of 1 K is equal to a temperature difference of 1 °C.
8. What happens to the kinetic energy of molecules as temperature approaches 0 K?
The kinetic energy of molecules tends to zero.
9. Is there any physical system at 0 K?
No, 0 K is a theoretical limit that cannot be practically reached due to the third law of thermodynamics.
10. Who proposed the Kelvin scale of temperature?
The Kelvin scale was proposed by **Lord Kelvin (William Thomson)**.
7. FAQ / Common Misconceptions
1. Is 0 K the same as 0 °C?
No, 0 K corresponds to -273.15 °C.
2. Does negative Kelvin temperature exist?
Not in classical thermodynamics. It exists only in special quantum systems with population inversion.
3. Why does the Kelvin scale start from 0 K?
Because it represents the lowest possible physical temperature, where thermal energy is minimal.
4. What is the significance of Kelvin temperature in thermodynamic equations?
All thermodynamic equations require temperature in Kelvin because it directly relates to molecular energy.
5. Can 273 K be used instead of 273.15 K?
Yes, in approximate calculations; but 273.15 K is the accurate conversion.
6. Does 100 K mean twice the temperature of 50 K?
In thermodynamics, yes — because Kelvin measures absolute temperature proportional to molecular energy.
7. Why is Celsius scale not suitable for thermodynamics?
Because it can have negative values, leading to incorrect physical interpretations in equations.
8. Can we say temperature measures heat?
No, temperature measures the *average kinetic energy* of molecules, not the total heat energy.
9. What happens to gas volume when temperature in Kelvin doubles?
According to Charles’ law, the volume also doubles (if pressure is constant).
10. What is the freezing point and boiling point of water on Kelvin scale?
Freezing point = 273.15 K, Boiling point = 373.15 K.
8. Practice Questions with Step by Step Solutions
Q1. Convert 30 °C to Kelvin.
Solution:
[T(K)] = [T(°C)] + [273.15] = [30 + 273.15] = [303.15 K]
Q2. Convert 400 K to Celsius.
Solution:
[T(°C)] = [T(K)] – [273.15] = [400 – 273.15] = [126.85 °C]
Q3. What is the absolute zero temperature in Celsius?
Solution:
[T(°C)] = [T(K)] – [273.15] = [0 – 273.15] = [-273.15 °C]
Q4. At what Kelvin temperature does water boil?
Solution:
Boiling point = [100 °C + 273.15] = [373.15 K]
Q5. If the temperature of a gas is raised from 27 °C to 127 °C, what is the ratio of final to initial absolute temperature?
Solution:
Initial [T₁ = 27 + 273.15] [= 300.15 K]
Final [T₂ = 127 + 273.15] [= 400.15 K]
Ratio [T₂/T₁ = 400.15/300.15] [≈ 1.33]
Hence, the temperature increases by about 33%.
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