Question

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?

Answer 1

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.