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26 August, 00:57

A closed system consisting of 4 lb of a gas undergoes a process during which the relation between pressure and volume is pVn 5 constant. The process begins with p1 5 15 lbf/in. 2, 1 5 1.25 ft3/lb and ends with p2 5 53 lbf/in. 2, 2 5 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. (c) Sketch Process 1-2 on pressure-volume coordinates.

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  1. 26 August, 01:28
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    V1=5ft3

    V2=2ft3

    n=1.377

    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=4lb*1.25ft3/lb=5ft3

    state 2

    V2=m. v2

    V2=4lb*0.5ft3/lb = 2ft3

    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 (15/53) / ln (2/5)

    n=1.377
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