In the case of hydrogen and oxygen, at NTP which of the following quantities is / are same?

(1) Average momentum per molecule 
(2) Average kinetic energy per molecule
(3) Kinetic energy per unit volume  
(4) Kinetic energy per unit mass

detailed solution

Correct option is B

vRMS=3RTM=3kTm ;     vAVG=8RTπM=8kTπmBoth these depend on nature of gas.Average momentum = mvAVG=8kTmπ (depends on nature of gas).Average kinetic energy per molecule =  12mvRMS2=12m3kTm=32kT (independent of nature of gas, depends on temperature).Kinetic energy per unit volume =  N12mvRMS2V=N12m3mkTV=32kTNVUsing PV = nRT and  n=NNA, we get,  n=NV=PNARTSince, pressure and temperature are same correspondingly, So, NV  is same.Kinetic energy per unit mass=   N12mvRMS2mass  of  gas=N12m3mkTmN=32mkT  (depends on nature of gas and temperature).