___ is zero for a cyclic process. 

The correct answer is ∆U.

Key Points

• In a cyclic process, the system returns to its initial state after completing the cycle, meaning the change in internal energy (∆U) is zero.
• Internal energy (U) is a state function, and its value depends only on the state of the system, not on the path taken to reach that state.
• The first law of thermodynamics states: ∆U = Q - W, where Q is heat added to the system, and W is work done by the system.
• For a cyclic process, the initial and final states are the same, so the net internal energy change (∆U) is zero, regardless of the values of Q and W.
• Examples of cyclic processes include Carnot cycles, Otto cycles, and Rankine cycles commonly used in thermodynamics and heat engines.

Additional Information

• Cyclic Process
  • A thermodynamic process where the system undergoes changes but eventually returns to its initial state.
  • Examples include processes in heat engines, refrigeration cycles, and power plants.
• Internal Energy (U)
  • The total energy contained within a system, including kinetic and potential energy at the molecular level.
  • It is a state function and depends only on the current state of the system (temperature, pressure, volume).
• First Law of Thermodynamics
  • Expresses the principle of conservation of energy: energy cannot be created or destroyed; it can only change forms.
  • Mathematically: ∆U = Q - W, where Q is the heat added to the system, and W is the work done by the system.
• Work (W) and Heat (Q)
  • Work is the energy transferred by a system to its surroundings due to macroscopic forces.
  • Heat is the energy transferred between systems due to a temperature difference.