A helium-filled toy balloon has a gauge pressure of 0.250 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?
Solution-
The volume of ballon in both cases will remain constant
Now given that
P1 = Patm + 0.250 = 1 + 0.25 = 1.25 atm
= 126656.3 N/m^2
P2 = Patm + 0 = 1 atm =101325 N/m^2
V1 = V2 = 10 L = 0.010 m^3
Now Internal energy for monoatomic gas is given by:
U1 = 3nRT/2 = 3*P*V/2
U1 = 3*P1*V1/2 = 3*126656.3 *0.010/2 =1899.84 J
U2 = 3*P2*V2/2 = 3*1.013*10^5*0.010/2 = 1519.5 J
Now the change in internal energy will be
dU = U2 - U1
dU =1519.5-1899.84
=-380.34 J
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