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Effect (W) from Temperature

  1. Jul 9, 2015 #1
    Let's say I have a cold bottle of water in a warm room (temperature is constant). Is it possible to calculate how long it will take for the water to reach a certain temperature? Do you guys know any formula for this? To be more general:

    What is the effect (W, J/s) that air in a certain temperature give an object surrounded by the air?
  2. jcsd
  3. Jul 9, 2015 #2


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    Yes, that's the big question. That depends of how the bottle is placed ( hanging in a wire / placed on a table ) and the shape of the bottle ( the relation: surface / volume is important ). This thermal flux coefficient is calculated with [ W/ΔTemperature ] as unit.

    Having found the thermal flux coefficient, you can make a differential equation.
  4. Jul 10, 2015 #3
    Thank you very much. Damn this is complex. Thought it would be like putting water on the stove and calculating when it will boil. Is it possble to calculate all of this theoretically, without experimenting? Are there any formulas out there? Tried looking all this up on Wikipedia, found this:


    151402b443097619f039039bd77bc675.png is the local heat flux density, W·m−2,
    ec2aa8ec0ee0f525bcf413c9fd8e87e9.png is the material's conductivity, W·m−1·K−1,
    c29d7b28f7486d0388b856afd85ddd30.png is the temperature gradient, K·m−1.

    Is this 151402b443097619f039039bd77bc675.png the thermal flux coefficient you mentioned? Note that the "m" in the explanation above isn't mass, it is meters. How do I apply a distance to my water? How can I take this further to calculate the time it takes to heat the water?

  5. Jul 10, 2015 #4


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    No, that's the flux density [ W/m2].
    I would say that k [ W/(K*m)] is closer. Actually the unit is [ (W*m)/(K*m2 ) ], meaning that k*area/thickness [ W/K ] gives the "thermal flux coefficient". ( I think it's a term of my own? ). You can also call it "the specific thermal conductiviy" for a material.
    No, but there are some "rule of thumb":
    If you have a black copper plate, about 3mm thick and mounted vertically, the thermal resistance will be θ = 600/A [ K/W ], where A is its area in cm2. But I don't think your bottle is black, and it's not made of copper.
    You must make some differential equation, modelling your bottle containing water. The solution to the equation will be an exponential function. Isolate t (time) in an equation.

    You may make a model by connecting a resistor and a capacitor in series and then charge the capacitor through the resistor. The current through the resistor is similar to the thermal flux, the voltage drop across the resistor is the temperature difference between air and bottle, the capacitor voltage is the temperature of the bottle.

    The bottle is a difficult problem because when the air heats up the water, the warm water will be gathered at the top of the bottle and vica versa. So speaking of temperature of the water, you could ask: Where in the bottle?
    Last edited: Jul 10, 2015
  6. Jul 11, 2015 #5
    Found this lecture from MIT, touched the subject a little, but went more to chemistry.

    Also: I feel like air of a certain temperature higher than an object should have a maximum amount of energy that it can give that object during a certain time, joules per second, W. Then as you say, the object may have certain proporities that make it less able to absorb that energy. But, that maximum W of the air of a certain temperature compared to the object, should be some sort of constant according to me. Been searching all over to find something, but does not really seem to find anyting of value.

    Thank you again, if you find more helpful information i will be glad. Will try to fix a equation of some sort.
    Last edited: Jul 11, 2015
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