Question

A flexible balloon contains 0.350 mol of an unknown polyatomic gas. Initially the balloon containing the gas has a volume of 6900 cm3 and a temperature of 30.0 ∘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

Given,

Cp=33.26 J/mol⋅K

γ=4/3

T1= 30+273=303K

T2=2 *T1= 2*303 = 606 K

T3=T1=303 K

1)

total heat Q supplied to the gas in the process

Q = Cp*n* $\Delta$ T
   = 33.26 x 0.350 x (606 - 303)
   = 3527.223 J

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2)

The total change in the internal energy ΔU of the gas is Zero .

Because the final temperature is the same as the initial temperature .

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3)

Total work(W) = 3527.223 J

The total work done by the gas must be equal to the
total heat supplied

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4)

final volume V

V2=2 V1 = 2*6900 = 13,800 cm^3

V3 = V2 (T2/T3)^[1/(γ-1)]

    = 13,800 (606/303)^3

   =110,400 cm^3

   =0.1104 m^3.