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!

Thermodynamics-a small doubt

  1. Jan 9, 2006 #1
    In thermodynamics it is said that S = dq/T. Then how can we say that S is directly proportional to T.
  2. jcsd
  3. Jan 9, 2006 #2


    User Avatar
    Gold Member

    That isn't exactly what is said. What is said is that
    The subscript "rev" means that the quantity dq represents the heat that would be transferred if the process were carried out reversibly.

    Also, S is not proportional to T. Suppose you heat a system reversibly at constant pressure. Then we have that
    The entropy change can be found by integrating the equation for dS. (You may notice that the as T approaches 0, dS seems to approach infinity. This is not actually the case since in reality the heat capacity is a function of temperature and the Debye extrapolation tells us that at very low temperatures the heat capacity varies like T^3) Suppose the heat capacity is constant over a temperature range of interest. Then
    [tex]\Delta S=\int_{T_1}^{T_2}\frac{C_p}{T}dT= C_p \int_{T_1}^{T_2}\frac{1}{T}dT=C_p\ln{\frac{T_2}{_T_1}[/tex]
    So in this case - as in most cases - S is not proportional to T, but does increase with incresing T.
  4. Jan 11, 2006 #3
    by what ratio does S increase with increase in T-Sorry Im confused.
  5. Jan 12, 2006 #4


    User Avatar
    Gold Member

    There is no definite ratio-it depends on the situation.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Thermodynamics-a small doubt
  1. Thermodynamics ! (Replies: 1)

  2. Thermodynamics ! (Replies: 1)

  3. Just a small doubt (Replies: 1)

  4. Thermodynamics ! (Replies: 1)

  5. Optics doubt (Replies: 3)