Calculating Heat Loss from an Insulated Cup

In summary, in order to find the heat loss due to conduction in an insulated cup containing coffee, we can use the equation P = kA(Th-Tc)/L, where k is the thermal conductivity, A is the area of the cup, Th is the temperature of the coffee, Tc is the temperature of the surroundings, and L is the thickness of the cup. In this case, the cup is a cube with a thickness of 0.5cm and a side length of 13.1cm. By converting the thermal conductivity from cal/s*cm*DegC to J/s*cm*DegC and multiplying the area by the number of sides (6), we can calculate the overall heat loss from the
  • #1
jdog6
17
0
Help! Heat Loss!

A cup of coffee (with a lid) is enclosed in an insulated cup 0.5cm thick in the shape of a cube 13.1cm on a side. The thermal conductivity of the cup is 0.0002 cal/s*cm*DegreeC. The temperature of the coffee is 87C and the temperature of the surroundings is 14C. Find the heat loss due to conduction. Answer in units of J/s.

I've tried P=kA(Th-Tc)/L ------> Energy transfer by conduction but somehow it's wrong?

I see no other way!

I know that:
k = 0.0002cal/s*cm*DegC which = 0.0008372J/s*cm*DegC
L=0.5cm
A=13.1cm*13.1cm (because cube)
A=171.61 cm^2
Th=87C
Tc=14C

ANY IDEAS?!
 
Last edited:
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  • #2
You're actually using kA(Th - Tc)/L , right?

Are you leaking Heat thru all 6 sides?

Did you convert from cal to J?

Are you using 13.1 cm as inside measure, or outside?
How do you know it's wrong?
 
  • #3
I know its wrong because my teacher said so :frown:

Yes I am using that equation.

I think I'm leaking on all sides

I did convert from cal to J.

And I'm using 13.1cm as an outside measure I believe.
 
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  • #4
Did you multiply the area of each side by 6 sides?
 
  • #5
Why x6 we are looking for overvall heat loss from this thermos like apparatus.
 
  • #6
you think Heat only leaks out the top?
How many sides does a cube have?
 
  • #7
Ok i understand but how do i fit it into the equation? k(6A)(Th-Tc)/L ?
 
Last edited:
  • #8
yea, or A = 6 s^2
 
  • #9
Correct! Thank you very much!
 

FAQ: Calculating Heat Loss from an Insulated Cup

What factors affect heat loss from an insulated cup?

The main factors that affect heat loss from an insulated cup are the material of the cup, the thickness of the insulation, the temperature difference between the inside and outside of the cup, and the surface area of the cup.

How do I calculate the heat loss from an insulated cup?

To calculate the heat loss from an insulated cup, you will need to know the thermal conductivity of the material, the thickness of the insulation, and the temperature difference between the inside and outside of the cup. You can then use the formula Q = kA(T1-T2)/d to calculate the heat loss, where Q is the heat loss, k is the thermal conductivity, A is the surface area of the cup, T1 is the temperature on the inside of the cup, T2 is the temperature on the outside of the cup, and d is the thickness of the insulation.

How does the material of the cup affect heat loss?

The material of the cup plays a significant role in heat loss. Materials with higher thermal conductivity, such as metal, will allow for more heat to transfer through the cup, resulting in higher heat loss. Insulating materials, such as foam or vacuum insulation, have lower thermal conductivity and will reduce heat loss.

Can I reduce heat loss from my insulated cup?

Yes, there are several ways to reduce heat loss from an insulated cup. You can use a cup with thicker insulation, choose a cup with a lower thermal conductivity material, reduce the temperature difference between the inside and outside of the cup, or decrease the surface area of the cup by using a smaller cup or adding a lid.

How does heat loss from an insulated cup impact the temperature of my drink?

The amount of heat lost from an insulated cup will directly affect the temperature of your drink. The more heat that is lost, the faster your drink will cool down. This is why choosing a well-insulated cup is crucial for keeping your drink at the desired temperature for a longer period of time.

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