Question

The root mean square value of the speed of the molecules in a fixed mass of an ideal gas is increasing by increasing:
A. The temperature while keeping the volume constant.
B. The pressure while keeping the volume constant.
C. The temperature while keeping the pressure constant.
D. The pressure while keeping the temperature constant.

Answer 1

The root mean square (RMS) is the concept that depends upon the Temperature, Gas constant and the Molar mass.

Complete step by step solution:
Given:
The Root Mean Square (RMS) is the square root of the ratio of product of the 3, gas constant and the temperature to the molar mass.
The equation of the Root Mean Square (RMS) can be written as $RMS = \sqrt {\dfrac{{3RT}}{M}}$.
Here, R is the Gas constant, T is the temperature in the body and the M is the Molar mass of the molecule.

According to the formula, it is clear that the root mean square value of the speed of the molecule in a fixed mass depends upon the Temperature and independent of any other factors like Pressure and the volume.

Therefore, the option is (a) and (c) are the correct that is that the fixed mass of an ideal gas increases with the increase in the temperature while keeping the volume and the pressure constant.

Note: Be careful at the equation terminology, the M is the molar mass whereas the R is not the resistance, it is gas constant. The value of the gas constant will depend upon the type of the gas and remain the same every time.