write the relation between RMS speed and average speed
Answers
Answer:
Root-mean-square speed, average speed and most probable speed : It measures the speed of particles in a gas. It is defined as the speed of particle is directly proportional to the square-root of temperature of gas and inversely proportional to the square-root of molar mass of gas
Answer : The ratio between root mean square speed average speed and most probable speed of the molecules in the sample of the gas is, 1.224 : 1.128 : 1
Explanation :
Root-mean-square speed, average speed and most probable speed : It measures the speed of particles in a gas. It is defined as the speed of particle is directly proportional to the square-root of temperature of gas and inversely proportional to the square-root of molar mass of gas.
The formula of root-mean-square speed, average speed and most probable speed are :
\nu_{rms}=\sqrt{\frac{3RT}{M}}\\\\\nu_{av}=\sqrt{\frac{8RT}{\pi M}}\\\\\nu_{mps}=\sqrt{\frac{2RT}{M}}
The ratio between the root-mean-square speed, average speed and most probable speed will be,
\nu_{rms}:\nu_{av}:\nu_{mps}\\\\\sqrt{\frac{3RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{2RT}{M}}\\\\\sqrt{3}:\sqrt{\frac{8}{\pi}}:\sqrt{2}\\\\1.732:1.596:1.414\\\\1.224:1.128:1
Therefore, the ratio between root mean square speed average speed and most probable speed of the molecules in the sample of the gas is, 1.224 : 1.128 : 1