A sample of ideal gas expands from an initial pressure and v

A sample of ideal gas expands from an initial pressure and volume of 32 atm and 1.0 L to a final volume of 4.0 L. The initial temperature is 300 K. If the gas is monatomic and the expansion isothermal, what are the final pressure final temperature, and work W done by the gas? If the gas is monatomic and the expansion adiabatic, what are final pressure final temperature, and W?

Solution

Pi = 32 atm = 32 x 101325 Pa

Vi = 1 L = 10^-3 m^3

Ti = Tf = 300 K

Vf = 4 litre = 4 x 10^-3 m^3

a) for isothermal expansion,

P V = constant

Pf = Pi/4 = 8 atm

b) for isothermal temp doesn\'t change.

Tf = Ti = 300 K

c) W = n R Tln(Vf/Vi) = Pi Vi ln(Vf/Vi)

W = (32 x 101325) (1 x 10^-3) ln(4/1) = 4494.9 J

d) for adiabatic process.

P V^y = constant

for monoatomic gas, y = Cp /Cv = 5/3 = 1.667
(32) ( 1)^(5/3) = Pf (4)^(5/3)

Pf = 3.17 atm

e) P V / T = constant

(32)(1) / 300 = (3.17)(4) / Tf

Tf = 118.9 K

f) W= Pi Vi^y ( Vf^(1-y) - Vi^(1-y)) / (1 - y)

    = (32 x 101325) ( 1 x 10^-3)^1.667 [ (4 x 10^-3)^-0.667 - (1 x 10^-3)^-0.667) ] / (1 - 1.667)
=1304.23 J

=