Question

A closed system consisting of 4 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.

Answer 1

a) V1 = 5 ft^3

V2 = 2 ft^3

b) n = 1.378

Step-by-step explanation:

Given data:

mass of gas = 4 lb

starting point

`p_1 = 15 lbf/in^2`

`v_1 = 1.25 ft^3/lb`

end point

`p_2 = 60 lbf/in^2`

`v_2 = 0.5 ft^3/lb`

Assume gas to be ideal

a) volume at point 1
`= v_1 * m`

`V_1 = 1.25 * 4 = 5 ft^3`

volume at point 2
`= v_2 * m`

`V_2 = 0.5 * 4 = 2 ft^3`

b) from ideal gas equation we have following equation

`(P_1)/(P_2) = [(V_2)/(V_1)]^n`

taking log on both side of equation

`ln [(P_1)/(P_2)] = n * ln [(V_2)/(V_1)]`

solving for n

`n = ( ln((15)/(53)))/( ln((2)/(5)))`

`n = (-1.262)/(-0.916)`

n = 1.378