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 determine the Kelvin temperature of the gas, you can use the formula for average kinetic energy:
K.E. = (3/2) * (nRT)
Where:
K.E. represents the average kinetic energy of the gas molecules,
n is the number of moles of gas (given as 1.9 mol),
R is the ideal gas constant (8.314 J/(mol·K)),
and T is the Kelvin temperature of the gas (the value we need to find).
Since the average kinetic energy of the gas molecules is equal to the kinetic energy of the bullet, we can equate them:
(3/2) * (nRT) = (1/2) * (mv^2)
Substituting the given values:
n = 1.9 mol
m = 8.0x10^-3 kg
v = 960 m/s
R = 8.314 J/(mol·K)
We can rearrange the equation to solve for T:
T = [(1/2) * (mv^2)] / [(3/2) * (nR)]
T = (m * v^2) / (3 * n * R)
Now we can substitute the given values and solve for T:
T = (8.0x10^-3 kg * (960 m/s)^2) / (3 * 1.9 mol * 8.314 J/(mol·K))
Performing the calculations:
T ≈ 403.300 K
Therefore, the Kelvin temperature of the gas is approximately 403.300 K.