Temperature Problem: Who Takes Hotter Coffee?

  • Thread starter neelakash
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In summary, if one adds cold cream to coffee that is already at room temperature, the coffee will get colder and lose more heat than if the cold cream was added to coffee that was colder than room temperature.
  • #1
neelakash
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Homework Statement



Two friends A and B receive cups of coffee those are at equal temperature.A adds some cool cream immediately and takes his coffee 10minutes later.B waits for 10 minutes,and adds the same amount of cool cream and begins to take.Decide who takes hotter coffee?

Homework Equations


The Attempt at a Solution



I cannot understand how should I use Newton's law of cooling here in this example.Please help me to start with.
 
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  • #2
Assuming that the cool cream is cooler than room temperature, friend B takes the hotter coffee.

Newton's law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the temperature of its surroundings.

The rate of change of temperature when the cream is immediately added has 10 minutes worth of effect on the temperature, combined with the temperature of its surroundings.

The rate of change of temperature has no time have much effect on the temperature of friend B's coffee, so only the surroundings' temperature cooled the coffee.
 
  • #3
neelakash said:
Newton's law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the temperature of its surroundings.
Right. The greatest difference leads to the greatest heat loss. So which situation gives the coffee the greatest difference in temperature with its surroundings?
 
  • #4
Does the solution not depend on the quantity of cream, if it is colder than the room temperature ?
Indeed, we could ask the (apparently) reverse problem:

Two friends receive each an ice cream. A adds a bit of hot cofee on his ice cream, ...
 
  • #5
I would assume that the cream is sitting in the refrigerator, waiting to be used when needed. (I suppose room temp cream would work just as well.)
 
  • #6
lalbatros said:
Does the solution not depend on the quantity of cream, if it is colder than the room temperature ?
Indeed, we could ask the (apparently) reverse problem:

Two friends receive each an ice cream. A adds a bit of hot cofee on his ice cream, ...

No, the ice cream question runs into phase transition issues. (ie: if you don't completely melt the ice cream, it will still have a temperature less than or equal to the melting point of ice cream.)

Anyway, it appears the answer to the question is the person who waited 10 minutes, then added cream. If you assume they both add the same amount of cold cream to the same amount of coffee.

The coffee that is not cooled earlier gets to radiate heat at a higher rate for the ten minutes, then it loses a fixed amount of energy to equilibriate the cold cream to whatever temperature.
 

1. How does temperature affect the taste of coffee?

Temperature can greatly impact the taste of coffee. Hotter coffee tends to have a stronger, more bitter taste, while cooler coffee can taste more acidic and sour. This is because temperature affects the rate at which different compounds in coffee are extracted, resulting in different flavor profiles.

2. Is there an ideal temperature for brewing coffee?

Yes, there is an ideal temperature for brewing coffee. The Specialty Coffee Association recommends brewing coffee between 195-205°F (90-96°C) for optimal flavor extraction. However, it ultimately depends on personal preference and the type of coffee being brewed.

3. Does the type of coffee bean affect the optimal brewing temperature?

Yes, different types of coffee beans may require different brewing temperatures for optimal flavor extraction. For example, darker roasts tend to have a stronger, more bitter taste and may require a slightly lower brewing temperature compared to lighter roasts.

4. How does the brewing method affect the ideal temperature for coffee?

The brewing method can greatly affect the ideal temperature for coffee. For example, pour over methods typically require a slightly lower brewing temperature compared to French press or espresso methods. This is because the contact time between the water and coffee grounds differs in each method, resulting in different flavor profiles.

5. Can the temperature of the environment affect the temperature of the coffee?

Yes, the temperature of the environment can affect the temperature of the coffee. For example, if the coffee is brewed in a cold room, it may cool down quicker compared to if it were brewed in a warm room. It is important to take into account the ambient temperature when brewing and serving coffee.

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