δu = q - w

Definition

The equation δu = q - w represents the first law of thermodynamics, which states that the change in internal energy (δu) of a system is equal to the heat added to the system (q) minus the work done by the system (w). This relationship highlights the conservation of energy principle, indicating that energy can be transformed from one form to another but cannot be created or destroyed. It emphasizes the interconnection between heat, work, and internal energy in thermodynamic processes.

5 Must Know Facts For Your Next Test

1. In this equation, 'q' can be positive if heat is added to the system and negative if heat is removed.
2. The term 'w' is considered positive when work is done by the system on its surroundings and negative when work is done on the system.
3. The first law of thermodynamics illustrates that any increase in internal energy comes from added heat or work done on the system.
4. This equation forms the foundation for understanding energy conservation in various thermodynamic processes, including isothermal and adiabatic processes.
5. It can also be applied to closed systems where no mass enters or leaves, allowing for simplifications in analysis.

Review Questions

• How does the first law of thermodynamics apply to a system undergoing a process where heat is added?
  • When heat is added to a system during a process, it increases the internal energy of that system. According to δu = q - w, if q is positive due to heat being added, this directly contributes to an increase in internal energy. If no work is done by or on the system (w = 0), then all the added heat contributes to raising the internal energy. Therefore, understanding how heat impacts internal energy is crucial in analyzing thermodynamic processes.
• Discuss how changes in work and heat affect internal energy based on the first law of thermodynamics.
  • Changes in work and heat are inversely related when considering internal energy. When work is done by the system (w > 0), it leads to a decrease in internal energy unless compensated by an equivalent amount of heat added (q). Conversely, if heat is absorbed (q > 0), it can increase internal energy even if some work is done. This dynamic interplay between q and w demonstrates how different forms of energy transfer influence a system's overall energy state.
• Evaluate a scenario involving both heat transfer and work done on a gas, analyzing how it demonstrates the principles behind δu = q - w.
  • Consider a gas in a closed container where it absorbs 100 J of heat while 40 J of work is done on it. According to δu = q - w, we would calculate δu as follows: δu = 100 J - (-40 J) = 140 J. This indicates that the internal energy of the gas increases by 140 J due to the combined effects of heat absorption and work done on it. This scenario illustrates how thermal interactions and mechanical actions together alter a system's internal energy, perfectly exemplifying the first law of thermodynamics.

Related terms

Internal Energy: The total energy contained within a system due to the kinetic and potential energies of its particles.

Heat Transfer: The movement of thermal energy from one object or system to another due to a temperature difference.

Work: The energy transferred when a force is applied to an object causing it to move, often represented in thermodynamics as work done by or on the system.