Final answer:
To double the rms velocity of nitrogen molecules enclosed in a vessel at 300 Kelvin, we need to calculate the change in internal energy of the nitrogen gas.
Step-by-step explanation:
The question asks how much heat is required to double the root mean square (rms) velocity of nitrogen molecules enclosed in a vessel at 300 Kelvin. To find the heat supplied, we need to calculate the change in internal energy of the nitrogen gas.
Using the formula for rms velocity, Vrms = √(3kT/m), where T is the temperature in Kelvin, k is the Boltzmann constant (1.38 x 10^-23 J/K) and m is the mass of a nitrogen molecule (28 atomic mass units), we can calculate the initial and final rms velocities. Doubling the rms velocity means increasing it by a factor of √2.
By using the equation for change in internal energy, ΔU = (3/2) nRΔT, where n is the number of moles, R is the gas constant (8.314 J/(mol·K)), and ΔT is the change in temperature, we can calculate the change in internal energy and the heat supplied.