1. What is the RMS speed of Helium atoms when the temperature of the Helium gas

Question

1. What is the RMS speed of Helium atoms when the temperature of the Helium gas is 290 K? (Possibly useful constants: the atomic mass of Helium is 4.00 AMU, the Atomic Mass Unit is: 1 AMU = 1.66×10-27 kg, Boltzmann's constant is: kB = 1.38×10-23 J/K.)

What would be the RMS speed, if the temperature of the Helium gas was doubled?

2. At least how many Calories does a mountain climber need to climb from sea level to the top of a 4.22 km tall peak assuming the muscles of the climber can convert chemical energy to mechanical energy with an efficiency of 14.0 percent. The total mass of the climber and the equipment is 78.6 kg. (Enter your answer as a number without units.)

Explanation / Answer

Here ,

Temperature , Ti = 290 K

RMS speed = sqrt(3 * 8.314 * 290/.004)

RMS speed = 1098 m/s

the rms speed at 290 K is 1098 m/s

for the double temperature

RMS speed = sqrt(3 * 8.314 * 290 * 2/.004)

RMS speed = 1552.8 m/s

the rms speed of the helium is 1552.8 m/s

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