The Kinetic Theory of Gases

Abstract

As stated previously Classical Thermodynamics is very much a mathematical discipline. Given that the defining equations are known, the theory is developed around multi-variable calculus. The theory is actually quite elegant, but it does not predict how to estimate or calculate the fundamental quantities or the properties that characterize them. For this, a transition to Statistical Thermodynamics is required. Statistical Thermodynamics starts with the kinetic theory of gases and treats fluids as made up of large assemblages of atoms or molecules. It can be a very detailed and extensive theory that extends well beyond the subjects of interest to this text. However, a smattering of Statistical Thermodynamics, including the kinetic theory of gases, will be useful for understanding a number of Classical Thermodynamics phenomena. A brief sojourn into the kinetic theory of gases is useful.

Problems

Problem 6.1: Estimate the rms velocity of a hydrogen molecule at STP and compare it with the speed of sound in hydrogen at STP.

Problem 6.2: Calculate the scattering cross section for the water molecule and the mean free path in water vapor at 500 K and 2 atmospheres.

Problem 6.3: Assume air to be composed of only nitrogen and calculate the mean free path for a nitrogen molecule in the standard atmosphere at 16 km altitude.

Problem 6.4: Given that the viscosity of air is 2.08E-05 N-s/m² at 350 K, and 1 atm, estimate its value at 10 atm and 1000 K.

Problem 6.5: Given that the thermal conductivity of water vapor at 1 atm and 400 K is 0.0261 W/m/K, estimate its value at 10 MPa and 700 K.