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Heat required at constant pressure

  1. Dec 24, 2006 #1
    1. The problem statement, all variables and given/known data
    1) How much heat energy must be added to the gaseous mixture consisting of 1 gm of Hydrogen and 1 gm of Helium to raise its temperature from 0 degree C to 100 degree C
    at constant pressure? Given that g1=1.41, g2=1.67

    2. Relevant equations

    Heat required = nC(p)dT

    3. The attempt at a solution

    Heat energy in Joules:

    Let C(p1), C(p2) and C(p) be the specific heat of Hydrogen, Helium and the mixture at constant pressure respectively. Let g1,g2 and g be the ratio of the specific heats at constant volume and pressure for Hydrogen, Helium and the mixture respectively. Here I have taken the value of the universal Gas constant[R] = 8.314 Joule/mole-K
    C(p1) = (g1 x R)/(g1 -1)
    = 28.59 J/mole-K
    C(p2) = (g2 x R)/(g2-1)
    = 20 .72 J/mole-K
    C(p) = {(n1 x C(p1)) + (n2 x C(p2))}/(n1 + n2)
    = 709.7 J/mole-K
    Let n1,n2 and n be the number of moles of Hydrogen, Helium and the mixture respectively.
    n1 = 0.5 moles
    n2 = 0.25 moles
    n = 0.75 moles
    Heat required = nC(p)dT
    = 53200 Joules = 12666 Calories

    Heat energy in Calories:

    Here I have taken the value of the universal Gas constant[R] = 1.99 Calorie/mole-K
    Heat required = 466 Calories
    Why do I get 2 different answers just because of change in units of R?
  2. jcsd
  3. Dec 24, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    Because your C(p) = 709.7 can't possibly be right. If the components have Cp of 28.59 and 20.72, the mixture must have Cp in between those values.

    The equation looks OK, so I guess you hit the wrong buttons on your calculator.
  4. Dec 24, 2006 #3
    U r right. What am I doing??Thanks.
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