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 that relates kinetic energy, number of moles, and temperature. The equation is:
KE = (3/2) * n * R * T
Where KE is the kinetic energy, n is the number of moles, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.
First, rearrange the equation to solve for T:
T = KE / [(3/2) * n * R]
Now, let's substitute the known values into the equation:
KE = kinetic energy of the bullet = 0.5 * m * v^2
= 0.5 * (6.6x10^-3 kg) * (670 m/s)^2
n = 1.3 mol
R = 8.314 J/mol·K
Substituting these values, we get:
T = (0.5 * (6.6x10^-3 kg) * (670 m/s)^2) / [(3/2) * 1.3 mol * 8.314 J/mol·K]
Simplifying the equation gives:
T = 1431.9 K
Therefore, the Kelvin temperature of the gas is approximately 1431.9 K.