Question

Which of the following is a correct statement for a thermodynamic system?

• A. The internal energy changes in all processes
• B. Internal energy and entropy are state functions
• C. Work is a state function
• D. The work done in an adiabatic process is always zero

Hint:

Remember the main state functions in thermodynamics: Pressure (P), Volume (V), Temperature (T), Internal Energy (U), Enthalpy (H), Entropy (S), and Gibbs Free Energy (G). The two main path functions are Heat (q) and Work (w).

Answer 1

The Correct Option is B

Step 1: Understanding State Functions and Path Functions.

• State Function: A property of a system that depends only on the current state of the system (e.g., temperature, pressure, volume, internal energy, entropy), not on the path taken to reach that state. The change in a state function depends only on the initial and final states.
• Path Function: A property that depends on the path taken between two states (e.g., heat, work).

Step 2: Evaluating each statement.
(A) The internal energy changes in all processes: This is incorrect. For example, in an isothermal process involving an ideal gas, the internal energy (which depends only on temperature for an ideal gas) remains constant (\(\Delta\)U = 0). Also, in a cyclic process, the system returns to its initial state, so the change in any state function, including internal energy, is zero.
(B) Internal energy and entropy are state functions: This is correct. Both internal energy (U) and entropy (S) are properties that depend only on the state of the system, not on how the system arrived at that state. Their changes (\(\Delta\)U and \(\Delta\)S) are determined solely by the initial and final states.
(C) Work is a state function: This is incorrect. Work (w) is a classic example of a path function. The amount of work done to get from state A to state B depends on the specific path followed.
(D) The work done in an adiabatic process is always zero: This is incorrect. An adiabatic process is one in which no heat is exchanged with the surroundings (q=0). According to the first law of thermodynamics, \(\Delta\)U = q + w. For an adiabatic process, this becomes \(\Delta\)U = w. Since the internal energy can change (e.g., by changing temperature), the work done is generally not zero. Work is only zero in a free expansion into a vacuum.
Step 3: Final Answer.
The correct statement is that internal energy and entropy are state functions.