Q.Distinguish carefully between heat, work and internal energy as they are used in thermodynamics, bringing out how each depends (or does not depend) on the particular process followed by the system.

Internal energy ($U$) is the total energy stored in a system's molecules -- kinetic energy of random motion plus potential energy of intermolecular forces (for an ideal gas, purely kinetic, depending only on temperature). It is a state function: its value, and hence any change $\Delta U$ between two states, depends only on those two states, never on how the system got from one to the other.

Heat ($Q$) is energy transferred between a system and its surroundings because of a temperature difference; work ($W$) is energy transferred because of a macroscopic force acting through a displacement (for a gas, $dW = P\,dV$). Both heat and work are path-dependent: taking a system between the very same two states by two different processes can (and generally does) involve different total amounts of heat absorbed and different total amounts of work done, even though $\Delta U$ between those two states is always identical either way. This is why it is meaningful to speak of "the internal energy of" a system, but meaningless to speak of "the heat contained in" or "the work contained in" a system -- heat and work are properties of a process, not of a state.

Define each quantity, then contrast state-function behaviour (internal energy) against path-dependence (heat, work) explicitly.

• Treating heat, work and internal energy as interchangeable terms for "energy in the gas."
• Failing to justify WHY heat and work are path-dependent while internal energy is not.