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  • A sample of neon gas (Ne) has an average kinetic energy that is four times the average kinetic energy of a sample of argon gas (Ar). If the temperature of the argon gas is 300n

A sample of neon gas (Ne) has an average kinetic energy that is four times the average kinetic energy of a sample of argon gas (Ar). If the temperature of the argon gas is 300 K, what is the temperature of the neon gas?

Option: 1

900 K


Option: 2

1000 K


Option: 3

1200 K


Option: 4

1300 K


Answers (1)

best_answer

The average kinetic energy of gas molecules is related to temperature through the following equation:

\frac{3}{2} k T=\frac{1}{2} m v^{2}

Where:  k is the Boltzmann constant - T is the temperature in Kelvin - m is the molar mass of the gas molecule in \mathrm{kg}-v is the root mean square speed of the gas molecules.

Since the molar mass of neon (Ne) is different from that of argon (Ar), the average kinetic energy of the two gases will be different even if they have the same temperature. Let's denote the temperature of the neon gas asT_{N e}.

We are given that the average kinetic energy of neon is four times that of argon:

\frac{3}{2} k T_{N e}=4 \times\left(\frac{3}{2} k T_{A r}\right)

Solving  T_{N e} we get, 

T_{N e}=4 \times T_{A r}

Substitute the value of T_{A r}(300 \mathrm{~K})

T_{N e}=4 \times 300 \mathrm{~K}

Calculating the value , T_{N e}=1200 \mathrm{~K}

The temperature of the Neon gas is 1200K. 

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