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Find Heat Energy Needed to Expand Gas to Triple Volume

  1. Mar 20, 2016 #1
    1. The problem statement, all variables and given/known data
    When 0.40 mol of oxygen(O2) gas is heated at constant pressure starting at 0 degrees C, how much energy must be added to the gas as heat to triple its volume? (The molecules rotate but do not oscillate)

    2. Relevant equations
    pV=nRT
    p1V1/T1=p2V2/T2
    Q=mcdT
    Value of Cp for Oxygen I used is 0.919 kJ/kg K
    3. The attempt at a solution
    I used the equation pV=nRT to get the value of pV at 273K which was pV=907.5. I tripled that value to get 2722.5. Then, using p1V1/T1=p2V2/T2, I plugged in the values to get the final temperature(819K). From that I used Q=mcdT which gave me the answer of 3211kJ. The answer in the back was 6.4 kJ.
     
  2. jcsd
  3. Mar 20, 2016 #2
    You must have missed a conversion factor somewhere, your temperatures are correct. For an isobaric process and constant heat capacity:
    [tex]Q= \Delta H = m C_P \Delta T[/tex]
    [tex]Q = 0.4 \ mol \left(0.032 \frac{kg}{mol} \right) \left( 0.919 \frac{kJ}{kg \cdot K} \right) (819.45 \ K - 273.15 \ K) = 6.426 \ kJ[/tex]
     
  4. Mar 20, 2016 #3
    My mistake was using gmol-1 instead of kgmol-1 for the molar mass. Thanks!!
     
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