The average kinetic energy of a molecule of a gas at 27 °C is 4.14 × 10–21 J. Calculate the temperature at which the average kinetic energy of a molecule of the gas will be 8.28 × 10–21 J. (JEE Main 2017)
The average kinetic energy of a gas molecule is given by:
E = \frac{3}{2}kT
where k is the Boltzmann constant and T is the temperature.
In this problem, we are given that the average kinetic energy of a gas molecule at 27 °C is 4.14 × 10–21 J. We can convert this temperature to Kelvin by adding 273 to get 300 K.
We can also find the Boltzmann constant by looking it up in a table. We find that k = 1.38 × 10–23 J/K.
We can now plug these values into the equation for the average kinetic energy to find the temperature at which the average kinetic energy of a molecule of the gas will be 8.28
