Question

A helium-filled toy balloon has a gauge pressure of 0.350 atm and a volume of 11.0 liters. How much greater is the internal energy (in J) of the helium in the balloon than it would be at zero gauge pressure?

Answer 1

Volume of ballon in both cases will remain constant

Now given that

P1 = Patm + 0.350 = 1 + 0.35 = 1.35 atm = 1.37*10^5 N/m^2

P2 = Patm + 0 = 1 atm = 1.013*10^5 N/m^2

V1 = V2 = 11 L = 0.011 m^3

Now Internal energy for monoatomic gas is given by:

U1 = 3nRT/2 = 3*P*V/2

U1 = 3*P1*V1/2 = 3*1.37*10^5*0.011/2 = 2.26*10^3 J

U2 = 3*P2*V2/2 = 3*1.013*10^5*0.011/2 = 1.67*10^3 J

Change in internal energy will be

dU = U2 - U1

dU = 2.26*10^3 - 1.67*10^3 = 590 J

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