The average translational kinetic energy of N2 gas molecules at approximately 86,485°C becomes equal to the kinetic energy of an electron accelerated from rest through a potential difference of 0.1 volt.
To determine the temperature at which the average translational kinetic energy of N2 gas molecules equals the kinetic energy of an electron accelerated through a potential difference of 0.1 volt, we can use the relationship between kinetic energy and temperature. The average translational kinetic energy (3/2k_bT) of gas molecules is related to temperature (T), where kB is the Boltzmann constant.
The kinetic energy of an electron accelerated through a potential difference (V) is given by eV, where e is the elementary charge. Setting these two expressions equal to each other, we get: 3/2kBT=eV
Now, rearranging the equation to solve for temperature (T), we get:
T= 2eV/3kb
Given kB=1.38×10^−23 J/K and V=0.1V, we can substitute these values to find T. The resulting temperature is approximately 86,485°C. Therefore, at this temperature, the average translational kinetic energy of N2 gas molecules matches the kinetic energy of an electron accelerated through a potential difference of 0.1 volt.