Question

Five molecules of a gas moving with speeds 1,2,3,4,5 km/s what is their root mean square speed

Answer 1

Answer : The value of the root mean square speed of the gas molecules is 3.32 km/s

Explanation : Given,

Four molecules of gas have speeds = 1 ,2, 3, 4 and 5 km/s

Root mean square speed : It is defined as the square root of the average of the square of speeds.

To determine the root mean square speed.

We will first determine the square, then average or mean of that and then finally we will determine square root.

So,

$\text{Mean square of speeds}=\frac{\text{Sum of square of speeds}}{\text{Total number of speeds}}$

$\text{Mean square of speeds}=\frac{1^2+2^2+3^2+4^2+5^2}{5}$

$\text{Mean square of speeds}=\frac{1+4+9+16+25}{5}$

$\text{Mean square of speeds}=11$

Now,

Square root of mean of speeds = $\sqrt{11}=3.32km/s$

Hence, the value of the root mean square speed of the gas molecules is 3.32 km/s