If a process is both endothermic and spontaneous then

Options

A. `Delta S gt 0`
B. `Delta S lt 0`
C. `Delta H lt 0`
D. `Delta G gt 0`

Answer

To solve the question, we need to analyze the conditions for a process that is both endothermic and spontaneous.

### Step-by-Step Solution:

1. **Understanding Endothermic Process**:
- An endothermic process is one that absorbs heat from its surroundings. This means that the change in enthalpy (ΔH) for the process is positive (ΔH > 0).

2. **Understanding Spontaneity**:
- A spontaneous process is one that occurs without needing to be driven by an external force. The spontaneity of a process is determined by the Gibbs free energy change (ΔG). For a process to be spontaneous, ΔG must be negative (ΔG < 0).

3. **Gibbs Free Energy Equation**:
- The Gibbs free energy change is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
- Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = absolute temperature (in Kelvin)
- ΔS = change in entropy

4. **Substituting Known Values**:
- Since the process is endothermic, we know that ΔH is positive (ΔH > 0).
- For the process to be spontaneous (ΔG < 0), we can rearrange the Gibbs free energy equation:
\[ \Delta G < 0 \implies \Delta H - T \Delta S < 0 \implies T \Delta S > \Delta H \]

5. **Analyzing Entropy Change (ΔS)**:
- For the inequality \( T \Delta S > \Delta H \) to hold true, ΔS must be positive (ΔS > 0). This means that the entropy of the system is increasing.

6. **Conclusion**:
- Therefore, if a process is both endothermic and spontaneous, the condition that must be true is that ΔS is greater than zero (ΔS > 0).

### Final Answer:
The correct condition for a process that is both endothermic and spontaneous is:
- ΔS > 0