A monatomic ideal gas is studied in two separate samples, X and Y
PHYSICS · Multi-part · CBSE · Physics · Kinetic Theory · Kinetic Theory
Problem
A monatomic ideal gas is studied in two separate samples, X and Y. Each sample contains the same number of moles of the gas in identical rigid containers. Sample X is held at 250 K; sample Y is held at 500 K.
(a) On a single set of properly labeled axes with relative speed on the horizontal axis and fraction of molecules on the vertical axis, sketch qualitative Maxwell–Boltzmann distributions for samples X and Y. Clearly indicate which curve corresponds to which sample.
(b) Using your sketch, identify which sample has the higher most-probable molecular speed and explain how the sketch supports your conclusion.
(c) Derive an algebraic expression for the factor by which the root-mean-square speed changes when the absolute temperature of a gas is doubled, holding molar mass constant.
(d) The molar mass of the gas is 20.0 g mol−1. Calculate the numerical root-mean-square speeds for samples X and Y, and verify that your results are consistent with the factor obtained in part (c).