In an isulated container water is stirred with a rod to increase the temperature. Which of the following is true?

Options

A. `Delta U = W ne 0, q = 0`
B. `Delta U = W = q ne 0`
C. `Delta U = 0, W = q ne 0`
D. `W = 0, DeltaU = q ne 0`

Answer

To solve the question regarding the scenario of stirring water in an insulated container, we can analyze the situation using the principles of thermodynamics, particularly the first law of thermodynamics.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have an insulated container with water being stirred. An insulated container means that no heat can enter or leave the system (Q = 0).

2. **Applying the First Law of Thermodynamics**:
- The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) plus the work done on the system (W):
\[ \Delta U = Q + W \]

3. **Identifying Heat Transfer (Q)**:
- Since the container is insulated, there is no heat transfer to or from the water. Therefore, we have:
\[ Q = 0 \]

4. **Identifying Work Done (W)**:
- When we stir the water, we are doing mechanical work on the system. This work is done by the stirrer, which increases the kinetic energy of the water molecules, leading to an increase in temperature. Thus, we can say:
\[ W \neq 0 \]
- The work done is positive because we are adding energy to the system by stirring.

5. **Calculating Change in Internal Energy (ΔU)**:
- Since Q = 0 and W is non-zero (positive), we can substitute these values into the first law equation:
\[ \Delta U = 0 + W \]
- This implies:
\[ \Delta U = W \]
- Therefore, the internal energy of the water increases due to the work done by stirring.

6. **Conclusion**:
- The temperature of the water increases due to the work done on it, even though no heat is added to the system. Thus, the statement that can be concluded is that the internal energy change (ΔU) is non-zero, and the temperature of the water increases.

### Final Answer:
The correct conclusion is that in an insulated container, when water is stirred, the internal energy of the water increases due to the work done on it, leading to an increase in temperature.