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!

Equilibrium temperature of a mixture

  1. May 22, 2014 #1
    1. The problem statement, all variables and given/known data
    2vnhu85.png

    2. Relevant equations
    [tex]Q = m c \Delta T \\
    Q = m L_v \\
    Q_{in} = Q_{out}[/tex]

    3. The attempt at a solution
    [tex]m_s c_s (100 - 8) + m_s L_v = m_s c_s (100 - T) + m_m c_s (T) \\
    5778.06 + 33900 = 5778.06 - 62.805 T + 418.7 T \\
    33900 = 355.895 T \\
    ∴ T = 95.25°C
    [/tex]
    Answer should be 90. This particular working is using 8°C as a base but I've with absolute temperatures and still got the same answer so I'm guessing my logic is flawed?
    Thanks
     
  2. jcsd
  3. May 22, 2014 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Your first equation doesn't appear to be set up correctly. The left side has two terms and the right side has two terms.

    Can you describe in words the meaning of each of the four terms in the equation?
     
  4. May 23, 2014 #3
    Qin = extra thermal energy the steam has over the milk + heat to be released when the steam condenses
    Qout = heat lost from the steam + heat gained by milk
     
  5. May 23, 2014 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The term

    m[itex]_{s}[/itex]c[itex]_{s}[/itex](100-8)

    implies that the mass of steam cools from 100 C to the temperature of the milk at 8 C after the steam condenses. This is clearly not the case, as the mixture will assume some as yet unknown temperature, which is higher than 8 C once thermal equilibrium is reached.

    Rather than use Q[itex]_{in}[/itex] = Q[itex]_{out}[/itex], which is somewhat vague for this type of problem, why not use instead Q[itex]_{lost-from-steam}[/itex] = Q[itex]_{gained-by-milk}[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Equilibrium temperature of a mixture
Loading...