The Thermodynamic Behavior of Gases

Variables and Constants

Ideal Gas An ideal gas is a gas in which the volume occupied by the gas particles is negligible compared to the volume occupied by the gas itself. There is little or no interaction between individual gas particles. Most gases behave as ideal gases as long as their temperature is not near the liquefication point and the pressure is not significantly higher than standard atmospheric pressure. 1. Temperature, T...Kelvin is required in all gas law equations. Variables 2. Volume, V...space occupied by a gas. A gas always fills any container into which it is placed. K=C+273

3. Pressure, P...due to collisions between gas particles and the walls of the container. Defined as the total force of all of the collisions divided by the surface area of the container.

4. Amount of gas a) mass -m, kg b) moles, n c) molecules, N

Constants

Definitions Monatomic gas... gas which is composed of single atoms He, Ne, Ar, Kr, Xe, and Ra Isobaric process…thermodynamic process in which the pressure is held constant Isochoric process…thermodynamic process in which the volume is held constant Isothermal process…thermodynamic process in which the temperature is held constant Adibatic process…thermodynamic process in which there is no heat flow.

Why is the constant pressure molar specific heat greater than the constant volume molar specific heat?

The state of a gas is determined by the values of the four variables: T, V, P and n (or m, or N). Once values of the four are given a unique state of the gas has been defined. Any three of the four variables are independent...can be arbitrarily set, the fourth variable is dependent and uniquely determined through an equation of state. An equation of state determines the relationship between the four variables of a gas. It causes one of the four variables to be dependent. The thermodynamics of gases is concerned with determining the states of a gas, the heat flow-Q, the work done-W, and the change in thermal energy-  U during thermodynamic processes.

Sign conventions for Work, Heat Flow, and Change in Thermal Energy

Gas Laws and the First Law of Thermodynamics

Ideal Gas Law Special Cases of the Ideal Gas Law

Dalton’s Law of Partial Pressures If an ideal gas is a homogeneous mixture of non-reacting gases (e.g. air), the total pressure is equal to the sum of the partial pressures of the component gases. The partial pressure of a component gas is the pressure it would exert if it were in the container alone.

Thermal Energy of an Ideal Gas The thermal energy, U of an ideal gas is a function of the Kelvin temperature alone. Therefore, in an isothermal process (T constant) the thermal energy must remain constant. The First Law of Thermodynamics If the total mechanical energy, E remains constant  E = 0:

Mathematical Description of the Thermodynamic Processes in Ideal Gases

Isobaric Process, P constant

Isochoric Process, V constant

Isothermal Process, T constant

Adiabatic Process, Q = 0

Graphical Representation of the Thermodynamic Processes in Ideal Gases

P-V Diagram of Isobaric and Isochoric Processes Isobaric expansion to V f, and T f. Isochoric process to P f, and T f.

P-V Diagram of Isothermal and Adiabatic Processes Isothermal Expansion to P 2,f and V f. Adiabatic Expansion to P 1,f, V f and T f.