98 The RMS velocity of a gas at 0°C is 2m/s. The
RMS velocity of the same gas at 819°C
Answers
Given - Vrms 1 = 2 m/s
Temperature 1 - 0° C
Temperature 2 - 819° C
Find - Vrms 2
Solution - Root mean square velocity of a gas is calculated by the formula -
Vrms = ✓(3RT/M). In the formula, R is gas constant, T is temperature in Kelvin and M is mass of gas.
The question considers velocity and temperature of same gas. Hence, mass and gas constant being same will be cancelled.
Temperature 1 - 373 K
Temperature 2 - 1092 K
Keeping the values in equation-
2/ Vrms 2 = ✓(373/1092)
2/ Vrms 2 = ✓0.34
2/ Vrms 2 = 0.584
Vrms 2 = 3.42 m/s
Hence, Root mean square velocity of gas at temperature 819 °C is 3.42 m/s
GIVEN :-
- RMS velocity of a gas at 0°C is 2m/s
TO FIND :-
- RMS velocity of the same gas at 819°C
SOLUTION :-
We have ,
T₁ = 0°C = 273K
T₂ = 819°C = 273 + 819 = 1092K
r₁ = 2m/s
r₂ = x (let)
Ratio of RMS velocities of same gas at two different temperatures is given by,
Where ,
- r₁ is RMS velocity of the gas at temperature T₁
- r₂ is RMS velocity of the gas at temperature T₂
∴ The RMS velocity of the gas at 819°C is 4 m/s
ADDITIONAL INFO :-
✺ Ratio of RMS velocities of different gases at same temperature is given by,
✺ RMS velocity of the gas when Pressure, Molecular weight and Volume are given is given by,