A1.2-mol sample of hydrogen gas has a temperature of 21 ∘c. part a what is the total translational kinetic energy of all the gas molecules in the sample? express your answer using two significant figures. k = 5 j previous answersrequest answer incorrect; try again; 4 attempts remaining part b how fast would a 75-kg person have to run to have the same kinetic energy? express your answer using two significant figures. v = m/s

A) The average translational kinetic energy of the molecules in a gas is given by:

where
is the Boltzmann's constant
T is the absolute temperature of the gas

In our problem, , so the average translational kinetic energy of the molecules is


We have 1.2 mol of this gas, and since one mole of ideal gas contains a number of molecules equal to Avogadro number, the total number of molecules in our gas is


So the total translational kinetic energy of all molecules of the gas is


B) The kinetic energy of a person is given by:

where m is the person's mass and v his velocity. The person has a mass of m=75 kg and its energy is equal to the energy of the gas, , therefore his velocity must be