1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time to take for water to cool down.

  1. Apr 13, 2012 #1
    My question refers to the cooling of water in a well-insulated , cylindrical cup that is opened at the top.

    0.336Kg of water at 84degCel is poured into the cup which is left to stand on a table at an ambient temperature of 25degCel. The specific heat capacity of water is 4150 J Kg^-1 K^-1 and the U-value is 10.64Wm^-2K^-1. The area of the water surface that is exposed to the surroundings air is 0.00447 m^2.

    So, how to calculate the time taken in seconds for the water to cool down to 46degCel?

    This is what I have done so far....

    Let x = (U-value)(Surface Area)/(mass)(Heat Capacity)
    Let y1 = 46DegCel (cool down temp)
    Let y2 = 84DegCel (Water temp)
    Let y3 = 25DegCel (Ambient tempt)
    Taking time to be T, so...

    T = -1/x log (y1-y3)/(y2-y3)
    = -13153 (sec)

    I got negative, so my guess something is wrong here. The formula is from my book. Need help....
     
  2. jcsd
  3. Apr 14, 2012 #2
    Have you studied Newtons Law of Cooling?
     
  4. Apr 14, 2012 #3
    I saw the mistake...it's suppose to be log base e thus the negative is cancelled out. Btw, ya I've studied Newton's Law
     
  5. Apr 14, 2012 #4

    gneill

    User Avatar

    Staff: Mentor

    Couple of things. First, the log should be the natural logarithm, loge not log10. Second, your argument for the log is less than one, so it should yield a negative value that is subsequently dealt with bu the "-" in front of 1/x.
     
  6. Apr 14, 2012 #5
    sorry i wasnt able see newtons law of cooling equation. You have written it in such a way that i thought you have written some other thing. I saw it now
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Time to take for water to cool down.
Loading...