Question 905: Thermodynamics & KTG

Question

The rms speed of a gas molecule is '$$\mathrm{V}$$' at pressure '$$\mathrm{P}$$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be

Accepted Answer

The root mean square (rms) speed of gas molecules is given by the equation:
$$V_{rms} = \sqrt{\frac{3 k_B T}{m}}$$
where:
$$V_{rms}$$ = rms speed
$$k_B$$ = Boltzmann constant
$$T$$ = absolute temperature
$$m$$ = mass of a gas molecule
It's important to note that the rms speed depends on the temperature and not directly on the pressure. As temperature remains constant in this problem (since it is specified "at the same temperature"), the rms speed of the gas molecule will not change when the pressure is increased.
As such, even if the pressure is increased by two times, the rms speed of the gas molecules will remain unchanged at the same temperature.
Hence, the correct option is:
Option A
$$\mathrm{V}$$

Answer

$$\mathrm{V}$$

Answer

$$\sqrt{2} \mathrm{~V}$$

Answer

$$\frac{V}{3}$$

Answer

$$\frac{V}{2}$$

Thermodynamics & KTG

The rms speed of a gas molecule is '$\mathrm{V}' at pressure '\mathrm{P}$'. If the pressure is increased by two times, then the rms speed of the gas molecule at the same temperature will be

Choose the correct answer: