Question

Which of the following quantities are thermodynamic state functions (ie value is independent of path taken between states)?
• Internal Energy (U)
• Heat (Q)
• Enthalpy (H)
• Work (W) Choose the correct answer from the options given below:

• A. B & D Only
• B. A, B & D Only
• C. B, C & D Only
• D. A & C Only

Hint:

State functions depend only on initial and final states. Examples: \[ U,\ H,\ S,\ P,\ V,\ T \] Heat and work are path functions.

Answer 1

The Correct Option is D

Concept: A thermodynamic state function is a physical quantity whose value depends only on:
• Initial state
• Final state and does not depend upon: \[ \boxed{ \text{Path followed during the process} } \] Examples of state functions:
• Internal energy
• Enthalpy
• Entropy
• Pressure
• Temperature

Step 1: Analyze Internal Energy \(U\). Internal energy represents:
• Total microscopic energy of the system. Its change depends only on:
• Initial state
• Final state Hence: \[ \boxed{ U \text{ is a state function} } \] Therefore Statement A is correct.

Step 2: Analyze Heat \(Q\). Heat is not stored inside the system as a property. Heat depends on:
• The process path
• Method by which energy transfer occurs Thus: \[ \boxed{ Q \text{ is a path function} } \] Hence Statement B is incorrect.

Step 3: Analyze Enthalpy \(H\). Enthalpy is defined as: :contentReference[oaicite:1]{index=1} Since:
• \(U\), \(P\), and \(V\) are state quantities, enthalpy also depends only on state. Therefore: \[ \boxed{ H \text{ is a state function} } \] Hence Statement C is correct.

Step 4: Analyze Work \(W\). Work done depends on:
• The actual thermodynamic path followed. For example:
• Different expansion paths give different work values. Hence: \[ \boxed{ W \text{ is a path function} } \] Thus Statement D is incorrect.

Step 5: Determine correct combination. State functions are: \[ U \text{ and } H \] Thus: \[ A \ \& \ C \ \text{Only} \]

Step 6: Choose the correct answer. Hence the correct option is: \[ \boxed{(4)} \] Final Conclusion: Thermodynamic state functions among the given quantities are: \[ \boxed{ \text{Internal Energy and Enthalpy} } \] Hence, the correct answer is: \[ \boxed{(4)} \]