Question

Question: What is the average translational kinetic energy of nitrogen molecules at 1600 K?

Short answer

Answer

The average translational kinetic energy of nitrogen moleculesis$3.31\times {10}^{-20}\text{J}$.

Step-by-step solution

Given data  

The temperature of the nitrogen gas molecules is 1600 K.

Understanding the concept

The expression for the average kinetic energy is given by,

$K_{avg}=\frac{3}{2}KT$

Here K is the Boltzmann constant, T is the temperature, K_avg is the average kinetic energy.

The value of k is equal to the$1.38\times {10}^{-23} J/molecule ·K$ .

Calculate the average translational kinetic energy

Using the expression of the kinetic average energy,

$K_{avg}=\frac{3}{2}KT$

Substitute $1.38\times {10}^{-23} J/molecule ·K$for k , 1600 k for T into the above equation,

$$\begin{gathered} K_{avg}=\frac{3}{2}\times 1.38\times {10}^{-23}\times 1600 \\ {K}_{avg}=3.31\times {10}^{-20}\text{J} \end{gathered}$$

Therefore the average translational kinetic energy of nitrogen moleculesis$3.31\times {10}^{-20}\text{J}$.