In: Physics
A flexible balloon contains 0.360 mol of an unknown polyatomic
gas. Initially the balloon containing the gas has a volume of 7.50
m3 and a temperature of 27.0 ∘C. The gas first expands
isobarically until the volume doubles. Then it expands
adiabatically until the temperature returns to its initial value.
Assume that the gas may be treated as an ideal gas with
Cp=33.26J/mol⋅K and γ=4/3.
What is the total heat Q supplied to the gas in the process? What
is the total change in the internal energy ΔU of the gas? What is
the total work W done by the gas? What is the final volume V?
m=0.360mol
V=7.50 m3
T=27 C = 300 K
V2=2V1
Cp=33.26J/mol⋅K
γ=4/3
Now
P1 x 7.5 = 0.360 x 8.314 x 300
P1 = 119.72 Pa
Substituting the values for the temperature
300/T2 = V1/(2V1)
T2 = 600 K
(a)
Qiso = 0.360 x 33.26 x 300 = 3592.08 J
Qad = 0
Therefore total heat supplied, Q = 3592.08 + 0 = 3592.08 J
(b)
Substituting the values for the work done
Wiso = 119.72 x (2V2−V1) = 119.72 x (4V1 - 3V1) = 119.72 x 3V1
Wiso = 119.72 x 3 x 7.5 = 2693.7J
Wad = (0.360 x 8.314/0.33) (600-300) = 2720.95 J
Substituting the values for the change in internal energy
Uiso = 3592.08 - 2720.95 = 871.13J
Uad =0 - 2720.95 = -2720.95 J
So the total energy, U = 871.13 - 2720.95 = -1849.82 J
(c)
The total work done, W = 2693.7J + 2720.95 J = 5414.65 J
(d)
The final volume of the gas can be calculated as
Vf = 122.55 m3
I hiope this will help you. have a good day. Thanks.