Graph Analysis: Temperature Function of Water Cooling in Freezer

Exponential Decay with Graph Interpretation

Choose the graph that best represents the following:

Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the graph that best represents the following:

Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).

2

Step-by-step solution

Since the freezing point of water is below 0, the temperature of the water must drop below 0.

The graph in answer B describes a decreasing function and therefore this is the correct answer.

3

Final Answer

WeatherTemperature'000

Key Points to Remember

Essential concepts to master this topic
  • Physical Process: Water temperature decreases exponentially toward freezer temperature
  • Graph Shape: Curve starts high and decreases rapidly, then levels off
  • Check: Temperature must drop below 0°C for freezing to occur ✓

Common Mistakes

Avoid these frequent errors
  • Choosing linear decrease instead of exponential decay
    Don't assume temperature drops at constant rate = wrong graph shape! Cooling follows exponential decay where temperature drops quickly at first, then more slowly as it approaches the freezer temperature. Always look for the curved decreasing function that levels off.

Practice Quiz

Test your knowledge with interactive questions

Does the function in the graph decrease throughout?

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FAQ

Everything you need to know about this question

Why doesn't the temperature drop in a straight line?

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Temperature change depends on the temperature difference between the water and freezer. When the difference is large (hot water), cooling is fast. As the water gets closer to freezer temperature, cooling slows down - creating a curved graph, not a straight line.

What does 'lukewarm water' mean for the starting point?

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Lukewarm water starts at a moderate temperature above room temperature (around 30-40°C). This means the graph should begin well above the freezer temperature and curve downward.

How do I know which direction the curve should go?

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Think about the process: water in a freezer gets colder over time. So temperature (Y-axis) must decrease as time (X-axis) increases. The curve slopes downward from left to right.

Why does the curve level off instead of going to zero?

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The water temperature approaches the freezer temperature (usually around -18°C), not absolute zero. Once frozen, the ice temperature stays close to the freezer temperature.

What if I can't tell the difference between the graphs?

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Focus on two key features: 1) Does it curve downward (exponential decay)? 2) Does it start high and end low? Only one graph will have both characteristics matching the cooling process.

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