Calculate wa, the work done by the gas as it expands along path a from v0 to va=rvv0. express wa in terms of p0, v0, and rv

Question

Calculate wa, the work done by the gas as it expands along path a from v0 to va=rvv0. express wa in terms of p0, v0, and rv

in progress 0
2022-04-09T06:45:59+00:00 2 Answers 0

Answers ( 2 )

  1. Eden
    0
    2022-04-09T06:47:10+00:00

    W= Integral of P dV
    PV = nRT
    P= PO VO/ V
    W= Integral of PO VO/ v dV
    W= PO VO In (Vf/VO)
    So we can say that,
    W= PO VO In Rv

  2. Violet
    0
    2022-04-09T06:47:15+00:00

    The work done by the gas is :

    Wa = Po Vo ( Rv – 1 )

    [tex]texttt{ }[/tex]

    Further explanation

    The Ideal Gas Law that needs to be recalled is:

    [tex]large {boxed {PV = nRT} }[/tex]

    P = Pressure (Pa)

    V = Volume (mu00b3)

    n = number of moles (moles)

    R = Gas Constant (8.314 J/mol K)

    T = Absolute Temperature (K)

    Let us now tackle the problem !

    [tex]texttt{ }[/tex]

    Complete Question:

    Calculate [tex]W_A[/tex], the work done by the gas as it expands along path A from [tex]V_0[/tex] to [tex]V_A = R_V V_0[/tex].

    Express [tex]W_A[/tex in terms of [tex]p_0 , V_0,[/tex] and [tex]R_V[/tex]

    Given:

    initial volume = Vo

    final volume = V_A

    constant pressure = p_o

    Asked:

    word done by the gas = W_A = ?

    Solution:

    Work done by the gas is the area under Pressure Vs Volume Graph.

    [tex]texttt{Work} = texttt{Area Under P Vs V Graph}[/tex]

    [tex]W_A = p_0 times ( V_A – V_0 )[/tex]

    [tex]W_A = p_0 times ( R_V V_0 – V_0 )[/tex]

    [tex]W_A = p_0 V_0 times ( R_V – 1 )[/tex]

    [tex]large {boxed {W_A = p_0 V_0 ( R_V – 1 )} }[/tex]

    [tex]texttt{ }[/tex]

    Learn more

    [tex]texttt{ }[/tex]

    Answer details

    Grade: High School

    Subject: Physics

    Chapter: Pressure

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