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Pressure/temperature energy question

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data

    A cylinder contains 260 L of hydrogen gas (H2) at 0.0° C and a pressure of 10.0 atm. How much energy is required to raise the temperature of this gas to 28.0° C? give answer in kJ.

    2. Relevant equations

    C=Q/(delta)T and/or PV=nRT

    3. The attempt at a solution

    using the first equation I got an answer of 63.5 which is incorrect. I am not sure how to place the given values into the second equation because I don't know what R stands for.

    the attempt with the second equation: (10.0 x 101.3)(260)=nR(28)
    1013*260=nR28
    263380=nR28
    9406.428571 =nR
    ????????????

    Thanks in advance.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 21, 2010 #2

    kuruman

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    The second equation (ideal gas law) says nothing about energy, so it is inappropriate for this question. You must use the first equation, but I am not sure you have written correctly. Look up in you textbook what equation you must use when you add heat to a gas at constant volume.
     
  4. Jan 21, 2010 #3
    That explains why it made no sense.

    I have another equation is it relevant?

    U=Q + W
     
  5. Jan 21, 2010 #4

    kuruman

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    More correctly ΔU = Q + W. That could be it because you are looking for Q. Note that the volume of the gas does not change, so W = 0 which means that ΔU = Q. Can you find an expression for ΔU?
     
  6. Jan 21, 2010 #5
    I found the equation

    (Delta)U = nC(sub V)*(Delta)T

    I have changed the T into Kelvin and plugged in the following numbers:

    (D)U = n(28.82)(301) = 8674.82

    I have to give the answer in kJ. If the answer I got correct how do I put it into the right form? What is the conversion?
     
    Last edited: Jan 21, 2010
  7. Jan 21, 2010 #6
    I subsequently found another version of the equation as written above but with C(sub p). Then I found that:

    Delta U= nC(sub p)*Delta T and worked out the problem as follows:
    U = 12.5 (28)=350

    Which one is the right one? Is there a right one?
     
  8. Jan 22, 2010 #7

    kuruman

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    You need to know what these equations mean and what the symbols stand for. You use CV when you add heat heat to the gas at constant volume and Cp when you add heat at constant pressure. Here you are adding heat at constant volume.

    In the expression Q = n CV ΔT

    n = number of moles - you need to find that.
    CV = specific heat at constant volume
    ΔT = change in temperature (it is not 301)

    When you put in all the correct numbers, the answer should come out in Joules. You can easily convert that to kJ at that point.
     
  9. Jan 22, 2010 #8
    Q= n Cv delta T

    n=3.348x10^-24 Cv= 10.144 T=48

    Q= (3.348x10^-24)(10.144)(48)

    Q= 1.630e^-21


    this seems rather small. I think I'm not calculating the temperature correctly.
     
    Last edited: Jan 22, 2010
  10. Jan 22, 2010 #9
    Do I have to use the 10.0 atm someplace?
     
  11. Jan 22, 2010 #10

    kuruman

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    Yes, this is extremely small. Please show exactly how you calculated n and the temperature change.
     
  12. Jan 22, 2010 #11
    calculating n
    molecular weight of hydrogen 2.016/6.022x10^23=3.34772501e^-24 I rounded this to 3.348

    Cv=10.144 (this is from a chart but I think it is for 25 degree C) so there is probably an error here but I don't know how to adjust it)

    Delta T=301-253=48
     
  13. Jan 22, 2010 #12

    kuruman

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    The number of moles is proportional to the total mass of the gas. Your calculation shows that any mass of gas will have the same number of moles. This is not correct. Use the ideal gas law to find the amount of gas (number of moles) that you have

    The temperature correction is not to worry about. The units of this are kJ/kg K. This means that if you use this number, you need to find the mass of the gas from the number of moles and express it in kilograms. Remember that 6.022x1023 molecules are one mole (n = 1).

    0 oC = 273 K, not 253 K.
     
  14. Jan 22, 2010 #13
    new calculations:

    Q= n Cv T

    n=(524.16) Cv=(10.144) Delta T=(28)

    Q=148878.2131

    To turn into kJoules = answer x 1000=148.878

    this seem more plausible to me. What do you think?
     
  15. Jan 22, 2010 #14

    kuruman

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    More plausible, yes, but you didn't show how you got the mass of the gas. CV=10.144 kJ/kg K. This means that if use this number, you need to convert the number of moles into kilograms. What is the meaning of n=524.16 and how did you get it?
     
  16. Jan 23, 2010 #15
    n=524.16 was found by multiplying the number of moles(2.016) by the 260L of hydrogen gas in the container from the original problem. I thought that might be how to find the value of n.

    moles were found by multiplying the atomic mass of Hydrogen (1.0079) by the 2 atoms (Hydrogen gas is H sub2 right?) that make up H gas and rounding to 3 decimal places.

    Thank you.
     
    Last edited: Jan 23, 2010
  17. Jan 23, 2010 #16

    kuruman

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    OK. You start with the ideal gas law pV = n R T.
    The number of moles is represented by the symbol n, so
    n = pV/RT

    In the above expression p is in Pascal, V is in m3 and T is in Kelvin. You need to do some conversions here before you plug in.

    Once you have a number for n, you know that one mole of hydrogen gas is 2 grams. Multiplying n by 2 gives you the mass of the gas in grams. You need to convert that to kilograms. Then you plug in the formula for Q.
     
    Last edited: Jan 23, 2010
  18. Jan 23, 2010 #17
    so then it should look like this:

    n=pV/RT

    n= (1.01325x10^6)(260)/R(28)


    with p in Pascals; 260 being the liters of gas (or should I use the 10.144?); 28 is the change in temperature and R? is R the constant volume?

    thanks. let me redo this. I somehow missed part of you message, sorry
     
    Last edited: Jan 23, 2010
  19. Jan 23, 2010 #18

    kuruman

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    The constant volume is represented by the symbol V (for volume) and in this case is 260 liters. It needs to be converted to cubic meters. It is not to be confused with the specific heat at constant volume CV.

    R is the universal gas constant. It is equal to 8.31 J/K.mole.
     
  20. Jan 23, 2010 #19
    after converting I have

    n=pV/RT

    (1.01325x10^6)(260)/(10.144)(3.0115x10^2)=86237.83645=n

    have I found n?
     
  21. Jan 23, 2010 #20
    Ok so I now have ALL the conversions and a new answer of n=9547107.31
     
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