Heat and Thermodynamics

rabiakhan.91

1. The problem statement, all variables and given/known data
A person walks into a bar and orders a drink made of 1.5oz of rum, 4 oz of coke, and 3oz of ice. How long does it take the drink to reach the room temperature of 22 degC


2. Relevant equations
q=mcΔT
q =mL where L is the latent heat of fusion
ΔQ/Δt=k(Tf-Ti)/L


3. The attempt at a solution
First we calculate the amount of heat needed to change ice into liquid using q=mL
That will happen through conduction and radiation. Conduction through the walls of the glass and radiation from the top of the glass.
and then i am stuck! what to do next

PAllen

If the room is assumed to be room temperature (duh), how does the heat flow rate from the glass change as the glass approaches room temperature?

RTW69

Get 1.5 oz of ethyl alcohol, 4 oz of coke, 3 oz of ice. Mix in a glass cup. Get thermometer and watch. Record the time to get to room temperature. This process will be more accurate than trying to model the heat transfer.

PAllen

Do you distinguish:

- reach room temperature within measurement error of some thermometer

and

- reach room temperature in exactly, per thermodynamic theory

What I'm getting at is that the question as given, without further qualification, seems like a trick question with an obvious answer.

gneill

I don't believe I've ever known a drink to last long enough to reach room temperature

RTW69

I would start by assuming a cylinder of uniform temperature and convection as being the most dominate heat transfer mechanism and see where you end up time wise. Then perhaps you look at evaporation effects from the open glass. If that doesn't get you close things get ugly.