A 10 meter by 5 meter by 5 meter room is filled completely with Helium gas (near
ID: 2026616 • Letter: A
Question
A 10 meter by 5 meter by 5 meter room is filled completely with Helium gas (nearly ideal). The mass of an individual atom can be calculated using the atomic mass number. For Helium this is 4u with u being the individual mass of a proton (or neutron) = 1.66x10-27 kg since Helium has 2 protons and 2 neutrons.
a. What is the mass of a single helium atom?
b.If the temperature of the room is lowered to 0°C, what is the rms velocity of the Helium atoms?
c.If the temperature of the room is to be increased to 50°C and the total mass of helium in the room is 50 kg, what amount of heat must be added?
Can you explain you answer? Thanks
Explanation / Answer
(a) The mass of the each helium atom is m = 4 ( 1.66*10-27 kg) = 6.64*10-27 kg ------------------------------------------ ------------------------------------------- (b) The rms velocity of the helium atom is vrms = sqrt ( 3kT /m ) = sqrt ( 3 (1.38*10-23 J /K)(273 K) / 6.64*10-27 kg ) = 1304 m/s -------------------------------------------------------- -------------------------------------------------------- (c) number of moles n = mass (m) / ( molar mass * avagadro number ) = ( ( 50 kg ) / (( 6.64*10-27 kg ) *(6.023*1023 ) = 1.25*104 mol The heat energy added Q = nCv dT = (1.25*104 mol )( 3/2 )(8.314 J/mol.K) ( 323 - 273K ) = 7.79*106 JRelated Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.