A glass tumbler containing hot water is kept in the freezer compartment of a refrigerator (temperature `lt 0^(@) C`). If you could measure the temperature of the content of the tumbler , which of the following graphs would correctly represent the change in its temperature as a function of time.

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the change in temperature of hot water in a glass tumbler placed in a freezer compartment, we need to analyze the process step by step.

### Step-by-Step Solution:

1. **Initial Condition**: The tumbler contains hot water. The initial temperature of the water is above 0°C.

2. **Placement in Freezer**: When the tumbler is placed in the freezer (which is at a temperature below 0°C), the heat from the hot water will begin to transfer to the colder environment of the freezer.

3. **Temperature Decrease**: As time progresses, the temperature of the water will start to decrease. This is because the water is losing heat to the surrounding cold air in the freezer. The temperature will continue to drop until it reaches 0°C.

4. **Reaching Freezing Point**: Once the temperature of the water reaches 0°C, it will remain at this temperature for a period of time. This is because the water is undergoing a phase change from liquid to solid (ice). During this phase change, the temperature remains constant at 0°C until all the water has turned into ice.

5. **Phase Change Completion**: After all the water has frozen into ice, the temperature of the ice will start to decrease further. The temperature will continue to drop as long as the ice remains in the freezer.

6. **Graph Representation**: The correct graph will show a decrease in temperature over time until it reaches 0°C, where it remains constant during the phase change, and then it will continue to decrease once the phase change is complete.

### Conclusion:
The correct graph that represents the change in temperature of the hot water in the tumbler as a function of time is the one that shows a decrease in temperature until it reaches 0°C, remains constant at 0°C during the freezing process, and then continues to decrease after all the water has turned to ice.