The literature has revealed that many students encounter substantial difficulties in applying the first law of thermodynamics. For example, university students sometimes fail to recognize that heat and work are independent means of energy transfer. When discussing adiabatic processes for an ideal gas, few students can correctly refer to the concept of "work" to justify a change in temperature. Some students adopt the notion that "collisions between molecules produce heat" to explain the rise in temperature for an adiabatic compression process. When explaining processes entailing temperature variation, students tend to adopt the ideal-gas law. Although most university students have acquired a reasonable grasp of the state-function concept, which is valid for variation of internal energy, they fail to grasp the concept that work depends not only on the states but also the processes. Thus, they are unable to use the first law effectively. In order to help students comprehend the meaning, usages, and value of the first law, and to realize that the ideal-gas law itself is insufficient to analyze many real-life examples, this paper introduces four examples, some of which can be demonstrated in the classroom. The examples have been devised and gradually modified over a period of several years based on implementation in a calculus-based introductory physics course. Details of when, how, and why each example is adopted, along with the students' pitfalls, are described below.