For a spontaneous process, the correct statement(s) is (are)

Options

A. `DeltaG_(system)_(T, P) gt 0`
B. `(DeltaS_(system)) + (DeltaS_("surroundings")) gt 0`
C. `(DeltaG_("system"))_(T,P) lt 0`
D. `(DeltaU_("system"))_(T,P) gt 0`

Answer

To determine the correct statements regarding spontaneous processes, we can analyze the thermodynamic principles involved, particularly focusing on the Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS).

### Step-by-Step Solution:

1. **Understanding Spontaneity**:
- A process is considered spontaneous if it occurs without needing to be driven by an external force. In thermodynamics, spontaneity is often assessed using the Gibbs free energy change (ΔG).

2. **Gibbs Free Energy Equation**:
- The relationship governing spontaneity is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
- Here, ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the absolute temperature, and ΔS is the change in entropy.

3. **Condition for Spontaneity**:
- For a process to be spontaneous, ΔG must be less than zero (ΔG < 0).

4. **Evaluating Statements**:
- **Statement A**: "ΔG system (T,P) > 0"
- This statement is incorrect because for a spontaneous process, ΔG should be less than zero.

- **Statement B**: "ΔS of system + ΔS of surrounding > 0"
- This statement is correct. The second law of thermodynamics states that the total entropy change (ΔS) of the universe (system + surroundings) must be greater than zero for a spontaneous process.

- **Statement C**: "ΔG of the system at given temperature and pressure < 0"
- This statement is also correct. For spontaneity, ΔG must be negative.

- **Statement D**: "ΔU of system at given temperature and pressure"
- This statement is incorrect in the context of spontaneity. The change in internal energy (ΔU) does not directly determine whether a process is spontaneous.

5. **Conclusion**:
- The correct statements regarding spontaneous processes are:
- Statement B: ΔS of system + ΔS of surrounding > 0
- Statement C: ΔG of the system at given temperature and pressure < 0

### Final Answer:
The correct statements are B and C.