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

## 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?

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

Hi there,

You are getting there. $$Q$$ 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 ($$J$$).

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

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

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.

Last edited by a moderator:
Redbelly98
Staff Emeritus
Homework Helper

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.

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

thanks

so did you get 0.0476 sec or did i do something wrong

Redbelly98
Staff Emeritus
Homework Helper

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

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

does 47.6sec sound right?

Redbelly98
Staff Emeritus