The key concepts need to solve this problem type are:

• Conservation of energy in the guise of the 1st law of thermodynamics (DU  = Q - W)
• The internal energy of a gas is given by U = 3nRT/2.  (The change in internal energy depends only on the initial and final temperatures of the gas.)
• The idea that the area under a graph of pressure vs. volume is the work done by or on the gas

The usual assumptions made in doing these problems are that:

• The processes are quasi-static. (system remains in equilibrium with its surroundings)
• The processes are reversible.  (no dissipative forces)

We sometimes also assume that the gases are only weakly interacting so that the ideal gas law applies.  However, this is not required.

Here's a plan for solving thermal process problems.

1.  Determine what is constant, if anything, in the problem.  The usual choices are volume (isochoric process), pressure (isobaric process), temperature (isothermal process), heat (adiabatic process).

2.  Determine the sign of those things that are not 0.  Use the sign conventions that heat added to a system and work done by a system are positive.

3.  Write the 1st law of thermodynamics and substitute those things that are 0 for the given problem situation.  Q is 0 for an adiabatic process, DU is 0 for an isothermal process, and W is 0 for an isochoric process (constant volume). DP is 0 for an isobaric process.

4.  Draw a P-V graph of the process.  Indicate with an arrow the direction that the process proceeds.  The graph provides a visual representation of the work done.  The arrow is a reminder of whether pressure and volume are increasing, decreasing, or staying the same.