A container holds 2.2 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of a 7.7x10-3 kg bullet with a speed of 650 m/s. What is the Kelvin temperature of the gas?

υ=2.2 mol, N₀=6.022•10²³ mol⁻¹,

k=1.38•10⁻²³ J/K

KE(ave) = υ•N₀•3kT/2
KE(bullet)=mv²/2
υ• N₀•3kT/2= mv²/2
T= mv²/3k• υ• N₀=
=7.7•10⁻³•650²/3• 1.38•10⁻²³•2.2•6.022•10²³=287 K

To find the Kelvin temperature of the gas, we can use the equation for average kinetic energy of a gas molecule:

KE = (3/2) * k * T

Where KE is the average kinetic energy, k is the Boltzmann constant, and T is the Kelvin temperature.

First, we need to find the average kinetic energy of the gas molecules. We are given that the total average kinetic energy of the gas molecules is equal to the kinetic energy of a bullet.

KE_gas = KE_bullet

Substituting the values:

(3/2) * k * T_gas = (1/2) * m * v^2

Where m is the mass of the bullet and v is its velocity.

Plugging in the values:

(3/2) * k * T_gas = (1/2) * (7.7x10^-3 kg) * (650 m/s)^2

Now we can solve for T_gas:

(3/2) * k * T_gas = (1/2) * (7.7x10^-3 kg) * (650 m/s)^2

Dividing both sides by (3/2) * k:

T_gas = (1/2) * (7.7x10^-3 kg) * (650 m/s)^2 / (3/2) * k

The Boltzmann constant, k, is approximately 1.38x10^-23 J/K.

Substituting the value of k:

T_gas = (1/2) * (7.7x10^-3 kg) * (650 m/s)^2 / (3/2) * (1.38x10^-23 J/K)

Now we can calculate T_gas:

T_gas = (1/2) * (7.7x10^-3 kg) * (650 m/s)^2 / (3/2) * (1.38x10^-23 J/K)

T_gas ≈ 8.94x10^22 K

Therefore, the Kelvin temperature of the gas is approximately 8.94x10^22 K.

To find the Kelvin temperature of the gas, we can use the formula for the average kinetic energy of a gas molecule:

Average Kinetic Energy = (3/2) * Boltzmann Constant * Kelvin Temperature

First, let's convert the mass of the bullet from grams to kilograms:

Mass of the bullet = 7.7x10^(-3) kg

Now, let's use the kinetic energy formula to calculate the kinetic energy of the bullet:

Kinetic Energy of the bullet = (1/2) * Mass * Velocity^2

Kinetic Energy of the bullet = (1/2) * (7.7x10^(-3) kg) * (650 m/s)^2

Now that we know the kinetic energy of the bullet, we can equate it to the average kinetic energy of the gas molecules:

(3/2) * Boltzmann Constant * Kelvin Temperature = Kinetic Energy of the bullet

Now, let's solve for the Kelvin temperature of the gas:

Kelvin Temperature = (2/3) * (Kinetic Energy of the bullet) / (Boltzmann Constant)

To find the value of the Boltzmann Constant, we can look it up:

Boltzmann Constant = 1.380649x10^(-23) J/K

Now that we have all the values, let's plug them into the formula and calculate the Kelvin temperature:

Kelvin Temperature = (2/3) * ((1/2) * (7.7x10^(-3) kg) * (650 m/s)^2) / (1.380649x10^(-23) J/K)

Calculating this expression will give us the Kelvin temperature of the gas.

formula to use is:

T= (mv^2)/u No 3k