The formula to calculate the Average Kinetic Energy (K) is:
\[ K = \frac{3}{2} \left( \frac{R}{N} \right) T \]
Where:
Let's say the temperature (\( T \)) is 300 K. Using the formula:
\[ K = \frac{3}{2} \left( \frac{8.314}{6.022 \times 10^{23}} \right) \times 300 \]
We get:
\[ K \approx 6.21 \times 10^{-21} \text{ J} \]
So, the Average Kinetic Energy (\( K \)) is approximately \( 6.21 \times 10^{-21} \) Joules.
Average kinetic energy is defined as the average energy contained within the movement of particles of a gas. It is a measure of the energy due to the random motion of the gas particles and is directly proportional to the temperature of the gas.
Definition: The average kinetic energy of a particle in a gas is related to its temperature.
Formula: \( \text{Average Kinetic Energy} = \frac{3}{2} k_B T \)
Example: \( \text{Average Kinetic Energy} = \frac{3}{2} \times 1.38 \times 10^{-23} \times 300 \)
Definition: Kinetic energy is the energy possessed by an object due to its motion.
Formula: \( \text{Kinetic Energy} = \frac{1}{2} m v^2 \)
Example: \( \text{Kinetic Energy} = \frac{1}{2} \times 10 \times 5^2 \)
Definition: The average kinetic energy of a gas molecule is directly proportional to the temperature of the gas.
Formula: \( \text{Average Kinetic Energy} = \frac{3}{2} k_B T \)
Example: \( \text{Average Kinetic Energy} = \frac{3}{2} \times 1.38 \times 10^{-23} \times 400 \)
