An insulated contianer, filled with water, contains a thermometer and a paddle wheel. The paddle wheel can be rotated by an external source. This apparatus can be used to determine.

Options

A. specific heat of water.
B. relation between kinetic energy and absolute temperature.
C. thermal conductivity of water.
D. mechanical equivalent of heat.

Answer

To determine the purpose of the insulated container filled with water, a thermometer, and a paddle wheel, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have an insulated container filled with water, which means that heat exchange with the environment is minimized.
- Inside the container, there is a thermometer to measure the temperature of the water.
- A paddle wheel is present, which can be rotated using an external source.

2. **Function of the Paddle Wheel**:
- When the paddle wheel is rotated, it does work on the water. This work done by the paddle wheel will cause the water to gain energy.
- Since the container is insulated, this energy will not escape to the surroundings, and the energy will be converted into thermal energy, thereby increasing the temperature of the water.

3. **Measurement of Temperature Change**:
- The thermometer will be used to measure the initial and final temperatures of the water.
- By knowing the amount of work done on the paddle wheel (which can be quantified), we can observe the corresponding change in temperature of the water.

4. **Relating Work Done to Heat**:
- The relationship between the work done on the paddle wheel and the heat gained by the water can be used to determine the mechanical equivalent of heat.
- The mechanical equivalent of heat is a concept that relates the amount of mechanical work done to the amount of heat produced.

5. **Conclusion**:
- Therefore, the apparatus can be used to determine the mechanical equivalent of heat, as it allows us to measure how much mechanical energy (work done by the paddle wheel) is converted into thermal energy (increase in temperature of the water).

### Final Answer:
The apparatus can be used to determine the mechanical equivalent of heat.

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