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Chapter 12: Problem 19

How does the average kinetic energy of a gas relate to its temperature?

Short Answer

Expert verified
The average kinetic energy of a gas is directly proportional to its absolute temperature. As the temperature increases, the average kinetic energy of the gas molecules also increases, which is represented by the formula \( KE = kT \), where k is the Boltzmann Constant (1.38 × 10^-23 J/K).

Step by step solution

01

Understanding Kinetic Energy

The Kinetic Energy (KE) of an individual gas molecule is given by the equation KE = 1/2mv^2, where m is the mass of the gas molecule and v is the velocity of the gas molecule. In a gas, all the molecules don't have exactly the same velocity, therefore we use the average kinetic energy.
02

Understanding Temperature relation with Kinetic Energy

The average kinetic energy (KE) of gas molecules is directly proportional to the absolute temperature (T) of the gas. This can be mathematically expressed as KE ∝ T. When the temperature of the gas increases, the velocity of the gas molecules also increases. Thus, there's more kinetic energy.
03

Deriving the Mathematical Relationships

Since the average kinetic energy is proportional to the temperature, we can express this relationship as KE = kT, where k is a proportionality constant called the Boltzmann Constant (k = 1.38 × 10^-23 J/K).

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