Which of the following processes must violate the first law of thermodynamics `(Q=W+DeltaE_(int)`)?

Options

A. `Wgt0 , Qlt0` and `DeltaE_(int)gt0`
B. `Wgt0 , Qlt0` and `DeltaE_(int)lt0`
C. `Wlt0 , Qgt0` and `DeltaE_(int)lt0`
D. `Wgt0 , Qgt0` and `DeltaE_(int)lt0`

Explanation

To determine which processes must violate the first law of thermodynamics, we need to analyze the given processes in the context of the equation:

\[ Q = W + \Delta E_{int} \]

Where:
- \( Q \) is the heat added to the system,
- \( W \) is the work done by the system,
- \( \Delta E_{int} \) is the change in internal energy of the system.

### Step-by-Step Solution:

1. **Identify the Processes**: We need to evaluate the processes provided in the question. Let's denote them as A, B, and C.

2. **Analyze Process A**:
- Assume \( Q_A < 0 \) (heat is removed from the system).
- If \( W_A > 0 \) (work is done by the system) and \( \Delta E_{int} > 0 \) (internal energy increases), we have:
\[ Q_A = W_A + \Delta E_{int} \]
- Since \( Q_A \) is negative and both \( W_A \) and \( \Delta E_{int} \) are positive, this leads to a contradiction. Thus, Process A violates the first law of thermodynamics.

3. **Analyze Process B**:
- Assume \( Q_B < 0 \) (heat is removed from the system).
- If \( W_B > 0 \) (work is done by the system) and \( \Delta E_{int} < 0 \) (internal energy decreases), we have:
\[ Q_B = W_B + \Delta E_{int} \]
- Here, \( Q_B \) can be negative if the decrease in internal energy is sufficiently large to offset the positive work done. Therefore, Process B does not necessarily violate the first law.

4. **Analyze Process C**:
- Assume \( Q_C > 0 \) (heat is added to the system).
- If \( W_C < 0 \) (work is done on the system) and \( \Delta E_{int} < 0 \) (internal energy decreases), we have:
\[ Q_C = W_C + \Delta E_{int} \]
- Here, if heat is added to the system while work is done on it and internal energy decreases, it creates a contradiction. Thus, Process C also violates the first law of thermodynamics.

5. **Conclusion**: The processes that violate the first law of thermodynamics are A and C.

### Final Answer:
Processes A and C must violate the first law of thermodynamics.