How Fast Does Water Cool in a Polystyrene Box?

In summary, we are trying to find the rate of temperature drop of a litre of water in a cubic polystyrene box at 90°C, with a wall thickness of 5mm and room temperature of 25°C. Using the equations P= (KAΔT)/diameter and E=mCΔT, we calculate the power of 0.00429W and the energy of 273J. From there, we find the time to be approximately 636363.6364 seconds and the rate of temperature drop to be 1.0214*10^(-6) °C/s. The units of thermal conductivity should be per m2.
  • #1
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Homework Statement


A cubic polystyrene box contains a litre of water at 90°C. It is 10cm wide and has a wall thickness of of 5mm. Room temperature is 25°C and the conductivity of polystyrene is 0.033W/m°C.
What is the rate of temperature drop of the water?

Homework Equations



P= (KAΔT)/diameter
E=mCΔT

The Attempt at a Solution



P= ((0.033)(0.000001)(65))/(0.005)=0.00429W
E=(1)(4.2)(65)=273
t=E/P, therefore:
t=636363.6364

ΔT/t=1.0214*10^(-6) °C/s




Not really sure if i did this right, and i feel really uncomfortable with my answers because
they're so small. especially the time. I feel i did something wrong with the Area.
 
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  • #2
What is the surface area of the box?
 
  • #3
Your units of thermal conductivity are incorrect. It should be per m2.
 
  • #4
Chestermiller said:
Your units of thermal conductivity are incorrect. It should be per m2.

No, W m-1 K-1 is correct.
 
  • #5
Oops. Sorry, you're right. My mistake.

Chet
 

FAQ: How Fast Does Water Cool in a Polystyrene Box?

1. What is the rate of temperature drop?

The rate of temperature drop refers to the speed at which the temperature of a substance or environment decreases over time.

2. How is the rate of temperature drop measured?

The rate of temperature drop is typically measured in degrees Celsius per unit of time, such as degrees Celsius per hour or degrees Celsius per minute.

3. What factors can affect the rate of temperature drop?

The rate of temperature drop can be influenced by a variety of factors, including the initial temperature, the type of substance or material, the surrounding environment, and any external factors such as wind or sunlight.

4. How does the rate of temperature drop relate to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. The rate of temperature drop is a result of the transfer of energy from a substance or environment to its surroundings, in accordance with this law.

5. Can the rate of temperature drop be controlled or manipulated?

Yes, the rate of temperature drop can be controlled or manipulated through various means such as insulation, heating or cooling systems, and external factors like windbreaks or shading. However, the overall rate of temperature drop is ultimately determined by the laws of thermodynamics and cannot be completely eliminated.

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