The first law of thermodynamics — common mistakes

Always pay very close attention to the wording of the question to correctly determine the signs for $Q$ and $W$. A common error is mixing up 'work done on the system' with 'work done by the system'. If the system does work (expands), $W$ is negative in the equation $\Delta U = Q + W$!

Internal energy is a state function because its value depends only on the current thermodynamic state of the system (e.g., its temperature, pressure, and volume), not on the path taken to reach that state. This means if a system returns to its initial state, its internal energy returns to its initial value, regardless of the processes it underwent.

Internal energy is the energy stored within a system due to the random motion and interaction of its particles. Heat (Q), on the other hand, is the transfer of thermal energy between systems or between a system and its surroundings due to a temperature difference. Heat is energy in transit, while internal energy is energy contained.

Yes, the First Law of Thermodynamics is a fundamental principle of energy conservation that applies to all thermodynamic systems, whether open, closed, or isolated, and to all types of processes, provided energy transfers are accounted for correctly as heat or work.

Certainly! For an isovolumetric process (constant volume), $W=0$ so $\Delta U = Q$. For an isothermal process (constant temperature), $\Delta U=0$ for an ideal gas, so $Q = -W$. For an adiabatic process (no heat transfer), $Q=0$ so $\Delta U = W$. For an isobaric process (constant pressure), all terms can be non-zero and $W = -p\Delta V$.