A container holds 1.3 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of a 6.6x10-3 kg bullet with a speed of 670 m/s. What is the Kelvin temperature of the gas?
To find the Kelvin temperature of the gas, we need to use the equation:
Average Kinetic Energy = (3/2) * k * Temperature
Where:
- Average Kinetic Energy is the total average kinetic energy of the gas molecules in the container
- k is the Boltzmann constant (k = 1.38 × 10^-23 J/K)
- Temperature is the Kelvin temperature of the gas.
First, let's find the average kinetic energy of the gas molecules:
Average Kinetic Energy = (3/2) * k * Temperature
We are given the average kinetic energy and we know the value of k, so we can rearrange the equation to solve for Temperature:
Temperature = (2/3) * (Average Kinetic Energy / k)
Temperature = (2/3) * (6.6x10^-3 kg * (670 m/s)^2 / 1.38 × 10^-23 J/K)
Now, let's calculate the temperature:
Temperature = (2/3) * (6.6x10^-3 * (670)^2 / 1.38 × 10^-23)
Temperature ≈ 9.74 × 10^3 K
Therefore, the Kelvin temperature of the gas is approximately 9.74 × 10^3 K.