How Long Until the Drink Reaches Room Temperature?

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SUMMARY

The discussion centers on calculating the time it takes for a drink composed of 1.5 oz of rum, 4 oz of coke, and 3 oz of ice to reach a room temperature of 22°C. Key equations mentioned include q=mcΔT for heat transfer and q=mL for the latent heat of fusion. Participants suggest practical experimentation with a thermometer to measure the time directly, emphasizing that modeling heat transfer may be less accurate than empirical observation. The conversation highlights the complexities of heat transfer mechanisms, including conduction, radiation, and convection.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the equations q=mcΔT and q=mL.
  • Knowledge of heat transfer mechanisms: conduction, convection, and radiation.
  • Basic experimental design skills for conducting temperature measurements.
NEXT STEPS
  • Research the effects of convection on heat transfer in liquids.
  • Learn about the latent heat of fusion and its implications in phase changes.
  • Explore the impact of evaporation on temperature changes in open containers.
  • Study the principles of thermodynamic equilibrium and its relevance to temperature measurements.
USEFUL FOR

This discussion is beneficial for students in thermodynamics, physics enthusiasts, and anyone interested in practical applications of heat transfer principles in everyday scenarios.

rabiakhan.91
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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
 
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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?
 
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.
 
RTW69 said:
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.
 
rabiakhan.91 said:

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 :biggrin:
 
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.
 

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