Advertisements
Advertisements
प्रश्न
Find the rms speed of hydrogen molecules in a sample of hydrogen gas at 300 K. Find the temperature at which the rms speed is double the speed calculated in the previous part.
Use R=8.314 JK-1 mol-1
उत्तर
Here,
Temperature of hydrogen gas, T = 300 K
Molar mass of hydrogen, M0 = 2 g/mol=0.002 kg /mol
We know,
\[C = \sqrt{\frac{3RT}{M_0}}\]
\[ \Rightarrow C = \sqrt{\frac{3 \times 8 . 3 \times 300}{0 . 002}}\]
\[ \Rightarrow C = 1932 . 6 {\text { ms }}^{- 1}\]
In the second case, let the required temperature be T.
Applying the same formula, we get
\[\sqrt{\frac{3 \times 8 . 3T}{0 . 002}} = 2 \times 1932 . 6\]
\[ \Rightarrow T = 1200 \text { K }\]
APPEARS IN
संबंधित प्रश्न
Which of the following gases has maximum rms speed at a given temperature?
Suppose a container is evacuated to leave just one molecule of a gas in it. Let va and vrms represent the average speed and the rms speed of the gas.
The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about
The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal g−1 °C−1 and 3.4 cal g−1 °C−1 respectively. The molecular weight of hydrogen is 2 g mol−1 and the gas constant, R = 8.3 × 107 erg °C−1 mol−1. Calculate the value of J.
Root mean square velocity of a particle is V at pressure P. If pressure is increased two times, then the rms velocity becomes ______.
A vessel of volume V contains a mixture of 1 mole of Hydrogen and 1 mole of Oxygen (both considered as ideal). Let f1(v)dv, denote the fraction of molecules with speed between v and (v + dv) with f2(v)dv, similarly for oxygen. Then ______.
Consider an ideal gas with following distribution of speeds.
| Speed (m/s) | % of molecules |
| 200 | 10 |
| 400 | 20 |
| 600 | 40 |
| 800 | 20 |
| 1000 | 10 |
Calculate Vrms and hence T. (m = 3.0 × 10−26 kg)
Consider an ideal gas with following distribution of speeds.
| Speed (m/s) | % of molecules |
| 20 | 10 |
| 400 | 20 |
| 600 | 40 |
| 800 | 20 |
| 1000 | 10 |
If all the molecules with speed 1000 m/s escape from the system, calculate new Vrms and hence T.
Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC ratio of their root mean square speeds at normal temperature and pressure is ______.
The rms speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are VH, VO, and `V_{CO_2}` respectively then ______.
The root means the square speed of smoke particles of mass 5 × 10-17 kg in their Brownian motion in air at NTP is approximate.
[Given k = 1.38 × 10-23 JK-1]
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and the oxygen molecule dissociates into atomic oxygen?
For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C; the rms speed of the molecules will be ______.
