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25 February, 05:21

A closed system consisting of 2 lb of a gas undergoes a process during which the relation between pressure and volume is pVn = constant. The process begins with p1 = 15 lbf/in. 2, ν1 = 1.25 ft3/lb and ends with p2 = 60 lbf/in. 2, ν2 = 0.5 ft3/lb. Determine (a) the volume, in ft3, occupied by the gas at states 1 and 2 and (b) the value of n.

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  1. 25 February, 05:37
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    V1=2.5ft3

    V2=1ft3

    n=1.51

    Explanation:

    PART A:

    the volume of each state is obtained by multiplying the mass by the specific volume in each state

    V=volume

    v=especific volume

    m=mass

    V=mv

    state 1

    V1=m. v1

    V1=2lb*1.25ft3/lb=2.5ft3

    state 2

    V2=m. v2

    V2=2lb*0.5ft3/lb = 1ft3

    PART B:

    since the PV ^ n is constant we can equal the equations of state 1 and state 2

    P1V1^n=P2V2^n

    P1/P2 = (V2/V1) ^n

    ln (P1/P2) = n. ln (V2/V1)

    n=ln (P1/P2) / ln (V2/V1)

    n=ln (15/60) / ln (1/2.5)

    n=1.51
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