Ch 18: Thermal Properties of Matter

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 15th Edition

Ch 18: Thermal Properties of Matter

문제 31a

18장, 문제 31a

Oxygen (O₂) has a molar mass of $32.0$ g/mol. What is the average translational kinetic energy of an oxygen molecule at a temperature of $300$ K?

검증된 단계별 안내

Start by understanding the concept of translational kinetic energy for a molecule. The average translational kinetic energy of a molecule in a gas is given by the formula:

\frac{3 k T}{2}

, where

k

is the Boltzmann constant and

T

is the temperature in Kelvin.

Identify the values needed for the calculation. The temperature

T

is given as 300 K. The Boltzmann constant

k

is approximately

1.38 \times 10^{- 23} J \cdot K - 1

Substitute the values into the formula for average translational kinetic energy:

\frac{3 \times 1.38 \times 10^{- 23} \times 300}{2}

Perform the multiplication in the numerator:

3 \times 1.38 \times 10^{- 23} \times 300

Divide the result from the previous step by 2 to find the average translational kinetic energy of an oxygen molecule at 300 K.

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Kinetic Theory of Gases

The kinetic theory of gases explains the behavior of gases in terms of the motion of their molecules. It states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. This concept is crucial for understanding how temperature affects the energy of molecules in a gas.

Translational Kinetic Energy

Translational kinetic energy refers to the energy due to the motion of a molecule moving from one place to another. For a single molecule, it is given by the formula (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin. This concept helps in calculating the energy associated with the movement of molecules at a given temperature.

Boltzmann Constant

The Boltzmann constant (k) is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. Its value is approximately 1.38 x 10^-23 J/K. Understanding this constant is essential for calculating the average kinetic energy of molecules in a gas at a specific temperature.