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Heat and Thermodynamics question

2016 · Q157
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Heat and Thermodynamics question

2016 · Q157

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1
A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?
  1. A
    P/(kT)
  2. B
    Pm/(kT)
  3. C
    P/(KTV)
  4. D
    mkT
View written solutionFree

Correct answer: B

As PV = nRT

⇒n=PVRT=massmolar mass \Rightarrow n = {{PV} \over {RT}} = {{mass} \over {molar\,mass}}⇒n=RTPV​=molarmassmass​   ...(i)

Density, ρ\rho ρ = massvolume=(molar mass)PRT=(mNA)PRT{{mass} \over {volume}} = {{\left( {molar\,mass} \right)P} \over {RT}} = {{\left( {m{N_A}} \right)P} \over {RT}}volumemass​=RT(molarmass)P​=RT(mNA​)P​
   [From eqn. (i)]

ρ=mPkT\rho = {{mP} \over {kT}}ρ=kTmP​    (∵R=NAk)\left( \because{R = {N_A}k} \right)(∵R=NA​k)

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