How Long Until the Drink Reaches Room Temperature?

[rabiakhan.91]

Homework Statement

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

Homework Equations

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

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]

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.

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]

Homework Statement

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

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.