Question

A closed system consisting of 4 lb of gas undergoes a process in which the relation between pressure and volume is pVn = constant. The process begins with p1 = 15 psi, v1 = 1.25 ft3/lb and ends with p2 = 53 psi and v2 = 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.

Answer 1

V1=5ft3

V2=2ft3

n=1.377

Step-by-step 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