A 1.00 mol sample of an ideal diatomic gas is confined in a cylinder fitted with a…
PHYSICS · Multi-part · CBSE · Physics · Kinetic Theory · Kinetic Theory
Problem
A 1.00 mol sample of an ideal diatomic gas is confined in a cylinder fitted with a frictionless, movable piston. The gas is taken from an initial state A (300 K, 1.00 atm) to a final state C in two separate steps:
• Step 1 (A → B): The gas is compressed isothermally until its pressure reaches 2.50 atm.
• Step 2 (B → C): The gas is heated at constant pressure (2.50 atm) until its temperature reaches 600 K.
Throughout the process the gas behaves ideally.
(a) Derive an algebraic expression for the factor by which the average intermolecular spacing changes in Step 1. Express your answer in terms of only the given numerical values.
(b) Calculate the numerical value of the spacing factor you derived in part (a).
(c) Derive an algebraic expression for the factor by which the collision frequency with the cylinder walls changes in Step 2. State any assumptions you make about the dependence of collision frequency on temperature and volume.
(d) Determine the overall factor (from state A to state C) by which the collision frequency changes relative to the initial state. Discuss whether the compression or the heating step has the greater influence on the final collision frequency.