How long will it take for coffee to reach the perfect temperature

In summary, the problem at hand involves determining the amount of energy and time required to restore a half-finished cup of coffee to its perfect temperature, given the initial temperature and volume of the coffee, as well as the rate of energy delivery of a microwave. Using the equation Q=mC(ti-tf), where Q is the amount of heat needed, m is the mass of the coffee, and C is its specific heat capacity, the energy needed to achieve the perfect temperature can be calculated. To determine the time needed, the power of the microwave, measured in watts, must be considered. Converting watts to joules per second, it can be used to calculate the time needed using the equation P = W/t or E/t. The
  • #1
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Homework Statement



4. Your half- finished cup of coffee has cooled down to a temperature Tc. You like your coffee to be at the perfect temperature Tp. You put your cup, containing x mL of coffee, into the microwave. Assume 1mL of coffee has a mass of 1g.

a. How much energy will it take to restore your coffee to its “perfect” temperature? Assume that coffee has the same thermal properties as water and that the cup itself gains negligible heat from the microwave.

b. The microwave delivers energy to the coffee at a rate of P watts. How much time should you set the microwave to heat your coffee to the perfect temperature?

c. If the microwave delivers 750W to the coffee, how long will it take to reheat the 140mL of the coffee from 22ºC to 83 ºC?

Homework Equations



Q=mC(ti-tf)

The Attempt at a Solution




okay i get the first bit

Q=m.4.186.(Tc-Tp)

in part b that gets me?

delivers energy to the coffee at a rate of P watts

how does that tell me how long it takes to heat up to
Q=m.4.186.(Tc-Tp)

if you get what i mean
 
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  • #2


Hi there,

You are getting there. [tex]Q[/tex] is the amount of heat the you need to "input" to your coffee to heat it up to your perfect temperature. This amount of heat will be given in joules ([tex]J[/tex]).

The power of your microwave only tells the rate of energy delivered to your coffee: [tex]750W = \frac{750J}{1s} = [/tex]

Does that help you a bit. Cheers
 
  • #3


but how do i know that it is 750j per sec...and not 750kj per min or something like that it just says the rate is 750watts
 
  • #4


Time is usually measured in seconds;

P = W/t or E/t,
where W and E are, respectively, the work done or energy transferred in time t (usually measured in seconds).

You can try this site if you want to know a little more about power:
http://en.wikipedia.org/wiki/Power_(physics [Broken])

Hope it helps.
 
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  • #5


ashvuck101 said:
but how do i know that it is 750j per sec...and not 750kj per min or something like that it just says the rate is 750watts

A Watt is 1 J/s, by definition.
 
  • #6


oh ok i should have look up watts up first i just thought it was a unit of energy
 
  • #8


so did you get 0.0476 sec or did i do something wrong
 
  • #9


That is too short. The actual time will be something reasonable ... reheating a cup of coffee in less than 1/20 sec in a microwave is not reasonable :smile:

Hint: check the units in your numbers, especially m and C.
 
  • #10


does 47.6sec sound right?
 
  • #11


Yes. :smile:
 

1. How long does it take for coffee to reach the perfect temperature?

The time it takes for coffee to reach the perfect temperature varies depending on several factors, such as the starting temperature of the coffee, the type of cup or mug it is in, and the ambient temperature of the room. On average, it can take anywhere from 3-5 minutes for coffee to reach the perfect temperature.

2. Is there an ideal temperature for coffee?

The ideal temperature for coffee is subjective and can vary from person to person. However, according to the Specialty Coffee Association, the optimal temperature range for serving coffee is between 195-205°F (90-96°C).

3. Can the type of cup or mug affect how quickly coffee reaches the perfect temperature?

Yes, the type of cup or mug can affect how quickly coffee reaches the perfect temperature. Ceramic or porcelain cups tend to retain heat better than glass or paper cups, so coffee in these types of cups will reach the perfect temperature faster.

4. Does stirring or adding cream and sugar affect the time it takes for coffee to reach the perfect temperature?

Yes, stirring or adding cream and sugar can affect the time it takes for coffee to reach the perfect temperature. Adding these ingredients can lower the overall temperature of the coffee, so it may take longer to reach the ideal temperature.

5. Can I use a thermometer to determine when my coffee has reached the perfect temperature?

Yes, using a thermometer can be a helpful tool in determining when your coffee has reached the perfect temperature. However, keep in mind that the temperature can vary slightly within the coffee, so it may not be exactly the same throughout the entire cup.

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