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

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(1) and (2)

(2) and (3)

(3) and (4)

All are true

answer is B.

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Detailed Solution

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).

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