# Which gas has the greatest kinetic energy? a) neon at a temperature of 200k b) neon at a...

## Question:

Which gas has the greatest kinetic energy?

a) neon at a temperature of 200k

b) neon at a temperature of 300k

c) neon at a temperature of 400k

d) neon at a temperature of 500k

e) neon at a temperature of 600k

f) none of the above (they all have the same kinetic energy)

## Average Kinetic Energy:

The formula for the average kinetic energy of the given gas molecules that we are going to use in this problem is shown below:

{eq}\displaystyle K.E.=\frac{3}{2}kT {/eq}, where,

• {eq}k {/eq} is the Boltzmann's constant.
• {eq}T {/eq} is the value of the temperature of the gas molecule.

## Answer and Explanation:

The given values of the temperatures of the neon gas are:

{eq}T_1=200\ K\\ T_2=300\ K \\ T_3=400\ K\\ T_4=500\ K\\ T_5=600\ K {/eq}

In the formula of the average kinetic energy of the gas molecule, {eq}\displaystyle \frac{3}{2}k {/eq} is the constant so the kinetic energy is directly proportional to the temperature.

{eq}\displaystyle K.E.\propto T {/eq}

The greater kinetic energy of the given gas will be obtained by the greater value of the given temperatures that means the kinetic energy will be greater at {eq}600 K {/eq}.

Thus, option (e) is correct.