How Fast Does Water Cool in a Polystyrene Box?

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Homework Help Overview

The problem involves a cubic polystyrene box containing water and seeks to determine the rate of temperature drop of the water as it cools from an initial temperature. The context includes thermal conductivity, dimensions of the box, and temperature differences.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to calculate the power transfer and energy change using given equations but expresses uncertainty about the correctness of their area calculation and the resulting small values for power and time.
  • One participant questions the surface area calculation, while another raises concerns about the units of thermal conductivity used in the calculations.

Discussion Status

The discussion is ongoing, with participants providing feedback on unit correctness and calculations. There is an acknowledgment of a mistake in unit interpretation, but no consensus on the overall approach or results has been reached yet.

Contextual Notes

Participants are navigating through potential errors in calculations and unit conversions, which may impact the understanding of the problem. The original poster's discomfort with the small numerical results suggests a need for further exploration of the assumptions made in the calculations.

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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.
 
Physics news on Phys.org
What is the surface area of the box?
 
Your units of thermal conductivity are incorrect. It should be per m2.
 
Chestermiller said:
Your units of thermal conductivity are incorrect. It should be per m2.

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

Chet
 

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