How Fast Does Water Cool in a Polystyrene Box?

[Undefeated]

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.

 

[DrClaude]

What is the surface area of the box?

 

[Chestermiller]

Your units of thermal conductivity are incorrect. It should be per m².

 

[DrClaude]

Your units of thermal conductivity are incorrect. It should be per m².

No, W m^-1 K^-1 is correct.

 

[Chestermiller]

Oops. Sorry, you're right. My mistake.

Chet