How Long Until the Drink Reaches Room Temperature?

In summary, the question asks how long it will take for a drink made of 1.5oz of rum, 4 oz of coke, and 3oz of ice to reach room temperature of 22 degC. The solution may involve calculating the heat needed to change ice into liquid, conduction and radiation from the glass, and considering the temperature of the room. However, the accuracy of the result may depend on whether the drink is assumed to reach exactly 22 degC or within a certain range due to measurement error or other factors.
  • #1
rabiakhan.91
12
0

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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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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:
 
  • #6
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.
 

1. What is heat?

Heat is a form of energy that is transferred between objects or systems as a result of a difference in temperature.

2. How is heat measured?

The standard unit for measuring heat is the joule (J). Other common units include the calorie (cal) and the British Thermal Unit (BTU).

3. What is the difference between heat and temperature?

Temperature is a measure of the average kinetic energy of particles in a substance, while heat is the transfer of thermal energy from one object to another.

4. What is the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another.

5. How does the second law of thermodynamics relate to heat?

The second law of thermodynamics states that heat will naturally flow from a higher temperature to a lower temperature, and that it is impossible for a heat engine to operate with 100% efficiency.

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