If hot water is mixed with cold water

Options

A. temperature first increases then becomes constant
B. temperature first decreases then become constant
C. increases continuously
D. first it is uncertain then become constant .

Answer

To solve the problem of what happens when hot water is mixed with cold water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Let the temperature of hot water be \( T_1 \).
- Let the temperature of cold water be \( T_2 \).

2. **Understand Heat Transfer**:
- When hot water is mixed with cold water, heat will flow from the hot water (higher temperature) to the cold water (lower temperature) until thermal equilibrium is reached.

3. **Establish Equilibrium**:
- At equilibrium, the final temperature \( T \) of the mixture will be somewhere between \( T_1 \) and \( T_2 \).
- The final temperature can be estimated using the formula:
\[ T = \frac{T_1 + T_2}{2} \]
- This indicates that the final temperature is the average of the two initial temperatures.

4. **Analyze Temperature Changes**:
- Initially, the temperature of the hot water \( T_1 \) will decrease as it loses heat to the cold water.
- The temperature of the cold water \( T_2 \) will increase as it gains heat from the hot water.
- Eventually, both temperatures will stabilize at \( T \).

5. **Conclusion**:
- Therefore, the temperature of the hot water first decreases as it loses heat, and then it stabilizes at the equilibrium temperature \( T \).

### Final Answer:
The correct conclusion is that the temperature of the hot water first decreases and then becomes constant. Thus, the answer is **Option B**.

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