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Ideal gas law - isovolumetric problem

  1. Sep 5, 2008 #1
    1. The problem statement, all variables and given/known data

    A gas sample enclosed in a rigid metal container at room temperature (20 C) has an absolute pressure p_1. The container is immersed in hot water until it warms to 40 C. What is the new absolute pressure p_2?

    Express your answer in terms of p_1

    2. Relevant equations

    PV = nRT where P is pressure in pascals, V is volume, n is the number of moles, R is constant = 8.314, T is temperature in kelvin

    convert celsius to kelvin
    K=C+273.15 where K is temp in kelvin, and C is temp in celsius

    3. The attempt at a solution

    since this problem is isovolumetric, the volume remains constant.

    p_1 = nRT_1/V where T_1 = 20C = 293 K assuming n,R,V are constant

    p_2 = nRT_2/V where T_2 = 40C = 313 K assuming n, R, V are constant

    how do i put p_2 in terms of p_1, do i just solve p_1 in terms of say V and substitute it in for V in the p_2 equation?

    doing so i get:

    V =nRT_1/p_1 = 293/p_1 asuming n and R are constant

    thus substituting V for V in the p_2 equation i get:

    p_2 = nRT_2/V = 313/(292/p_1) = 313p_1/292

    is that correct? i'm almost certain it is not correct.
     
  2. jcsd
  3. Sep 5, 2008 #2

    LowlyPion

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    Homework Helper

    That looks right. For such a question though - where you have an isobaric or isothermal you can just use the simple ratio. (You can always divide an equation by an equation.)

    [tex]\frac{P_1V_1}{P_2V_2} = \frac{nrT_1}{nrT_2}[/tex]

    In your case it Volume stays the same n the same and r the same so:

    [tex]\frac{P_1}{P_2} = \frac{T_1}{T_2} = \frac{293}{313}[/tex]
     
  4. Sep 6, 2008 #3

    Redbelly98

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    Another way to set it up, and which may be easier to remember, is to solve the ideal gas equation for R:

    [tex]
    R = \frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_2}
    [/tex]

    or in other words

    [tex]
    \frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_2}
    [/tex]

    Then you cancel all the quantities that are equal (in this case V and n) and go from there.
     
  5. Sep 6, 2008 #4
    the thing is when tried (313p_1)/292, it was incorrect and it stated that "your answer either contains an incorrect numerical multiplier or is missing one."

    noticed how i entered the denominator as 292 as opposed to 293, would that be the reason why it is incorrect?
     
  6. Sep 6, 2008 #5

    Redbelly98

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    It is incorrect by a very small amount, 0.3%. Why don't you try with the correct numbers and see what happens? Also, you could try dividing 313/293 on a calculator, and use that number times p_1.
     
  7. Sep 6, 2008 #6
    yes i tried it with 293 as the denominator. it was correct

    thanks for your help
     
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