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Homework Help: Thermodynamics change in internal energy

  1. Jun 10, 2010 #1
    1. A gas bottle with a volume of 0.1 m3 contains 0.4 kg of a gas at a pressure of 7
    MN/m2 and a temperature of 150 ºC. For this gas Cp = 10.54 kJ/kg K. Calculate
    the changes in internal energy when temperature is raised to 500K
    Given answer: 362 kJ




    2. pV=mRT pv=RT
    mCpdT=dH
    mCvdT=dU
    dq-dw=du




    3. so i've been struggling with this for a while. i know that du=dq as there is no net work when volume is constant.
    initially i used p1V1/mT1=R and then i used Cp=R+Cv to find Cv. From there i used the equation mCvdT=dU. however this doesnt give the correct answer.

    ive been trying a few other ways as well but they havent worked. is there some assumption i can make etc...?
     
  2. jcsd
  3. Jun 17, 2010 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Try calculating the number of moles using n = PV/RT with units in MKS and a gas constant of R = 8.314 J/K mol. I assume 7 MN/m^2 means 7x10^6 Pa.

    Then work out the ratio of moles to kg. to determine what the Cp is in terms of J/mole K. Subtract R from that to get Cv.

    I get n = 199 moles and Cv = 12.87 J/mol K, which gives an answer:

    [tex]\Delta U = nC_v\Delta T = 199 \times 12.87 \times 77 = 197.2 KJ[/tex]

    So I think the answer given is wrong.

    AM
     
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