A container holds 1.9 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of a 8.0x10-3 kg bullet with a speed of 960 m/s. What is the Kelvin temperature of the gas?
do I use the formula?
T= (mv^2)/u No 3k
To find the Kelvin temperature of the gas, you can use the equation:
T = (2/3) * (K.E. / N.A.)
Where:
T is the temperature in Kelvin
K.E. is the kinetic energy of the total gas molecules in Joules
N.A. is Avogadro's number, equal to 6.022 x 10^23 molecules/mol
First, let's calculate the kinetic energy of the 8.0x10^-3 kg bullet. The kinetic energy formula is:
K.E. = (1/2) * m * v^2
Where:
K.E. is the kinetic energy in Joules
m is the mass of the bullet in kg
v is the speed of the bullet in m/s
Plugging in the values, we get:
K.E. = (1/2) * 8.0x10^-3 kg * (960 m/s)^2
Now, solve for K.E.:
K.E. = (1/2) * 8.0x10^-3 kg * (960)^2 m^2/s^2
Next, let's calculate the total kinetic energy of the gas molecules in Joules. Since the total kinetic energy is equal to the kinetic energy of the bullet, we have:
K.E. (gas) = K.E. (bullet)
Now we can substitute the calculated value of K.E. (bullet) to find K.E. (gas):
K.E. (gas) = (1/2) * 8.0x10^-3 kg * (960)^2 m^2/s^2
Now, calculate the total kinetic energy of the gas molecules.
Once you have the total kinetic energy of the gas molecules, divide it by Avogadro's number (6.022 x 10^23 molecules/mol) to get the average kinetic energy per molecule.
Lastly, multiply the average kinetic energy per molecule by 3/2 (which is equivalent to 2/3) to get the temperature in Kelvin using the equation T = (2/3) * (K.E. / N.A.).
This will give you the Kelvin temperature of the gas.