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.

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