Many studies have shown that pre-university students have substantial learning difficulties related to heat, temperature, and related concepts. However, very few investigations have been reported that focus on student learning of thermal physics concepts at the university level. Here we report on an investigation of reasoning regarding heat, work, and the first law of thermodynamics among students in an introductory calculus-based general physics course. Responses to written questions by 653 students in three separate courses were very consistent with results of detailed individual interviews carried out with 32 students in a fourth course. Although most students seemed to acquire a reasonable grasp of the state function concept, it was found that there was a widespread and persistent tendency to improperly over-generalize this concept to apply to both work and heat. A large majority thought that net work done and/or net heat absorbed by a system during a cyclic process must be zero, while only 20% or fewer were able to make effective use of the first law of thermodynamics even after instruction was completed. Students' difficulties seemed to stem in part from the fact that heat, work, and internal energy all share the same units. Results were consistent with those of previously published studies of students in U.S. and European universities, but portray a pervasiveness of confusion regarding process-dependent quantities that was previously unreported. The implication is that significant enhancements of current standard instruction may be required for students to master basic thermodynamic concepts.