during one of our helium balloon launches the conditions at the ground were: tem

Question

during one of our helium balloon launches the conditions at the ground were: temperature was 21.4 degrees celsius, air density was 1.29 kg/m^3 helium density was 0.1786 kg/m^3 and the atomospheric pressure was 1.10 X 10^5 pascals. the balloons radius at the ground was 1.35 meters. the conditions when the balloon reached maximum altitude were: temperature was -20.5 degrees celsius, pressure was 900 pascals. assume the balloon contains only helium, none of the helium escapes, the balloon is spherical and is in thermodynamic equilibriumwith the surrounding atomosphere both on the ground and then again at maximum altitude with the surrounding atomosphere. assume that the atomosphere obeys the ideal gas law. to attach our payload to the balloon cord, we use a circular bass rod which has an initial length of 0.425 meters and a radius of 0.005 meters. the young's modulus for brass is 9.00 X 10^10 N/m^2.

5. calculate the number of helium atoms in the balloon.

6. calculate the root mean squared velocity of the helium atoms in the balloon on the ground, before launch.

7. calculate the temperature at the balloons maximum altitude in kelvins.

8. calculate the balloons volume at its maximum altitude.

Explanation / Answer

6) P*V=n*R*T

V=n*R*T/P=1*8.314*(21.4+273)/1.1*10^5=0.0225m^3

Mass=density*V=0.1786*0.0225=3.9741*10^-3Kg

Vrms=3*k*T/m=3*1.38*10^-23*(21.4*273)/3.9741*10^-3 =1.7512*10^-9m/s

7) T=-20.5+273=252.5K

8) V= 1*8.314*252.5/900=2.3325m^3

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