At what temperature is the root mean square ...

Kinetic Theory

Question : 9 of 14

Marks: +1, -0

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at –20°C? (atomic mass of Ar = 39.9 u, of He = 4.0 u).

Solution:

Here, atomic mass of argon

M_1 = 39.9

Atomic mass of helium He = 4.0

Let

C_1

and

C_2

be the rms velocities of argon and helium at temperature

T_1

K and

T_2

K respectively.

We know that rms speed is given by

C=\sqrt{\frac{3RT}{M}}

;

C_{1}=\sqrt{\frac{3RT_{1}}{M_{1}}}=\sqrt{\frac{3RT}{39.9}}

;

C_{2}=\sqrt{\frac{3RT_{2}}{M}}=\sqrt{\frac{3R \times 253}{4}}

Since

C_1 = C_2

\sqrt{\frac{3RT}{39.9}}=\sqrt{\frac{3R \times 253}{4}}

\Rightarrow T=\frac{39.9 \times 253}{4}=2523.7\,\text{K}

Go to Question:

Prev Question

Next Question