# Rate of Temperature Drop

1. Feb 19, 2013

### Undefeated

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

P= (KAΔT)/diameter
E=mCΔT

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 19, 2013

### Staff: Mentor

What is the surface area of the box?

3. Feb 19, 2013

### Staff: Mentor

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

4. Feb 19, 2013

### Staff: Mentor

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

5. Feb 19, 2013

### Staff: Mentor

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

Chet