# A question for all you coffe connoisseurs out there =)

I've always chuckled when I look up in my classroom and see the poster my physics teacher owns asking "How long would you have to yell to heat up a cup of coffe?". It would take an impracticle amount of time for a single person, however, with a twist this question could turn into quite the amusing experiment (granted it would take an enormous group of people). I figured you forum helpers must get bored every now and then, so I have a question for you! Yes, this is a spin on things, a pop-quiz from a student for all you teachers out there ;)

My question to you is:

How many people would have to yell for 60 sec to heat up an 8oz cup of coffe from room temperature (70°F) to a toasty 70°C? (Note: The average person yells at about 80 decibles)

Assume a perfect transfer of energy from your yell to the coffee, a perfectly insulated cup that will never let any heat escape, and an unending even stream of energy.

Cant you just feel your tastebuds tingling with excitement!?

Be sure to post your:

1. Givens and Unknowns

## Homework Equations

3. Work and solution

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My class hasn't covered themodynamics, or sound yet, but I dont want everyone thinking I'm secretly trying to get a homework answer! So heres my attempt... I'll be researching as I go so dont hold it against me! I might need some help at various stages in my problem. =)

1) G/U:
V=8oz
Ti=21.1°C
Tf=70°C
Δt=60s
1 Ounce = 0.0000295735296 Cubic Meters

2) Equations:

°C = 5/9 (°F-32)
Density = m/v

3) Work and Solution:

°C= 5/9 (°F-32)
°C= 5/9 (70-32)
°C= 21.1
Ti=21.1°C

(8oz) (0.0000295735296) = 0.0002365882368 m3 = 2.4e-4 m3

Density = m/V
m=Density * V
m=Density * (2.4e-4 m3)

Hmmmm, I'm stuck here. Am I missing data? Cant calculate mass if I dont have the density of water at 21.1°C. Are there ways to calculate the density of water at 21.1°C? Or is this a measured value that I'd have to add to my question?

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Borek
Mentor
You can safely assume 1 g/mL, even if it is not exact, it is close to reality.

For a very high precision you should check in density tables (but in this case it would be a waste of time).