A flexible balloon contains 0.400 mol of an unknown polyatomic gas. Initially th

Question

A flexible balloon contains 0.400 mol of an unknown polyatomic gas. Initially the balloon containing the gas has a volume of 6800 cm3 and a temperature of 22.0 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/molK and =4/3.

Part A

What is the total heat Q supplied to the gas in the process?

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Part B

What is the total change in the internal energy U of the gas?

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Part C

What is the total work W done by the gas?

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Part D

What is the final volume V?

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A flexible balloon contains 0.400 mol of an unknown polyatomic gas. Initially the balloon containing the gas has a volume of 6800 cm3 and a temperature of 22.0 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/molK and =4/3.

Part A

What is the total heat Q supplied to the gas in the process?

Q =   J  

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Part B

What is the total change in the internal energy U of the gas?

U =   J  

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Part C

What is the total work W done by the gas?

W =   J  

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Part D

What is the final volume V?

V =   m3  

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Explanation / Answer

P1*V1 = n*R*T1

P2*v2 = n*R*T2

for isobaric process

P1 = P2

also given v2 = 2v1

v2/v1 = = T2/T1

T2 = 2T1 = 2*(273+22) = 590 K

P1 = n*R*T1/v1 = 0.4*8.314*(273+22)/(6800*10^-6) = 144272.35 m^3

+++++++++++++++++++++++++++++

Qtot = Qiso + Qadia

Qtot = n*Cp*dT + 0

Qtot = 0.4*32.36*(590-295) = 3818.48 J

++++++++

dUtot = dUiso + dUadia

dU = n*cV*(T2-T1) + n*Cv*(T2-T1) = 0

++++++++++++

W = Wiso + Wadia

v2 = 2v1

v2 - v1 = v1

Wiso = P*(V2-v1) = 144272.35*6800*10^-6 = 981.05 J

Wadia = n*R*(T3-T2)/(1-r)

T3 = T1 = 295 K

gamma = r = 4/3

W = 0.4*8.314*(295-590)/(1-4/3) = 2943.16 J

Wtot = 981.05+2943.16 = 3924.21 J    <<<<<<-----------answer

+++++++++++++++++=

T2*V2^(r-1) = T3*V3^(r-1)

590*(2*6800)^(4/3-1) = 295*V3^(4/3-1)

V3 = 108800 cm^3 <<<------answer

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