Simple heat transfer problem and temperature change

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Discussion Overview

The discussion revolves around a heat transfer problem involving a polypropylene solid and its temperature change when exposed to air. Participants explore the application of heat transfer equations and Newton's law of cooling, focusing on unit conversions and the implications of different heat transfer coefficients.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The initial calculation for temperature change is based on the formula Q = c m (T1-T0), with specific heat capacity and mass provided.
  • One participant points out the importance of unit conversions, specifically noting that 1 gram is not equal to 0.1 kg.
  • Another participant recalculates using consistent units, converting specific heat capacity to J/kg/K and finds a similar result.
  • There is a discussion about the area used in the calculations, with a participant confirming that 0.5 cm² is equivalent to 5*10^-5 m².
  • A participant questions the validity of the heat transfer coefficient for polypropylene, suggesting a potentially different value of 24 W/m² K, which could significantly alter the temperature change result.
  • One participant notes that heat loss by radiation is being ignored, mentioning the emissivity of polypropylene and suggesting that it may be necessary to consider which mode of heat loss would dominate.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the heat transfer coefficient and its impact on the calculations. There is no consensus on the correct value for h, and the discussion remains unresolved regarding the dominant mode of heat loss.

Contextual Notes

Limitations include potential inaccuracies in the heat transfer coefficient and the exclusion of radiation heat loss from the calculations. The discussion also highlights the importance of consistent unit usage throughout the problem.

theodore100
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Homework Statement


What is the expected temperature change during one second of a polypropylene solid with mass 0.1 g at 105 degC to air at 20 degC

Homework Equations


heat transfer: Q= c m (T1-T0)
where Q = amount of heat
c = specific heat capacity = 1.8 J/g/K
m = mass
T1-T0 = change in temperature

Newton's law thermal cooling:
Q = -h.A.dT(t)

Q = heat lost
h = heat transfer coefficient for polypropylene = 0.2
A = area, small object = approx. 0.5 cm^2
Temperature differential, constant at 105-20

The Attempt at a Solution


T1-T0 = Q / c m = Q / 1.8 * 0.1

Therefore:

T1-T0 = (-0.2 * 5*10^-5 * 85) / (1.8 * 0.1) = 4.7 * 10^-3 degC

i.e. a very very small temperature drop in one second. Does this look right?

Thanks.
 
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Hi theodore100, Welcome to Physics Forums.

Be careful with your unit conversions. 1 gram is not 0.1kg.
 
Hi and thanks for the welcome.
I have got my units a bit mixed up, but the 0.1 is for the c * m calculation, c being in units of J/g/K. I will try it again with everything in Kg.
 
I get the same answer:
c in J/kg/K = 1800

T1-T0 = (-0.2 * 5*10^-5 * 85) / (1800 * 1*10^-4) = -0.0047
 
I'm guessing that the area has to be in m and 0.5 cm^2 is 5*10^-5 m^2 ?
 
Okay, provided that your units are in order, then your result looks good.

This presumes that the constant h really is the heat transfer coefficient for polypropylene to air (I've seen similar values for heat conductivity for polypropylene and it's curious that they would be the same value). Were you given units for h?
 
No, I wasn't given h, I googled it.. so yes, it might be wrong.
 
ok, this is interesting.. it might be more like 24 W/m^2 K
so the answer could be as high as 0.564 which sounds more realistic. I think I have the right approach, which is the main thing. Thanks.
 
Okay.

I should also note that heat loss by radiation is being ignored. Emissivity of PP is pretty high, around 0.97 if I recall correctly. You might check to see which mode of heat loss would dominate.
 

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