Question

A helium-filled balloon has a volume of 0.010 m3. The temperature in the room and in the balloon is 20∘C. What is the thermal energy of the helium in the balloon? Assume that due to stretching of the balloon the pressure inside it is 1.1 atm.

Answer 1

root-mean-square velocity:
v = √(3RT/M),
where v is velocity, R is universal gas constant, T is temperature (absolute), and M is molar mass.
v = √( 3 * 8.314 J/mol/K * 293 K / (4g/mol * 1kg/1000g) )
v = 1351 m/s
Thermal energy is equal to the kinetic energy:
KE = 1/2 m v²
PV = nRT
n = PV/RT
n = (1.1 atm * 10 L) / (0.0821 L atm / K / mol * 293 K)
n = 0.4572797 mol
m = n * M = 0.457 mol * 4 g/mol = 1.82911 g

KE = 1/2 m v²
KE = 1/2 (0.00182911 kg) (1351 m/s)²
KE = 1670 J