Final answer:
The equation v_rms = sqrt{3k_BT/m} is valid only for ideal gases and considers the mass of a single molecule and absolute temperature in Kelvin.
It holds true for different gases given these variables are accounted for, and v_rms is proportional to the square root of the temperature, contrary to being independent of temperature.
Step-by-step explanation:
To verify that vrms = sqrt{frac{3kBT}{m}} is valid or not, we should discuss the following aspects:
- a) The given equation is valid only for ideal gases: This is true. The root mean square speed (vrms) equation is derived under the assumption that we're dealing with an ideal gas where the molecules do not interact with each other except for elastic collisions and the volume of the molecules themselves can be neglected compared to the volume of the container.
- b) The equation is incorrect without knowledge of the specific gas: This is false. The specific gas is not required to be known because the equation for vrms includes the variable 'm', which is the mass of a single molecule of the gas, and 'T' which is the absolute temperature in Kelvin. Both variables account for the differences between different gases.
- c) The equation holds true for any type of gas: This is false. The equation is specifically derived for ideal gases and does not necessarily hold true for real gases, especially under conditions where the ideal gas assumptions break down, such as high pressures or low temperatures.
- d) The root mean square speed is independent of temperature: This is incorrect. The root mean square speed is directly proportional to the square root of the temperature, as indicated by the T variable in the equation. As the temperature increases, vrms also increases.