NEET-XII-Physics
24: Kinetic Theory of Gases
- #5Equal masses of air are sealed in two vessels, one of volume V0 and the other of volume 2V0. If the first vessel is maintained at a temperature 300 K and the other at 600 K, find the ratio of the pressures in the two vessels.Ans : Let the pressure and temperature for the vessels of volume V0 and 2V0 be P​1, T1 and P2 , T2, respectively.
Since the two vessels have the same mass of gas, n1 = n2 = n.
`` {T}_{1}=300\,\mathrm{\,K\,}``
`` {T}_{2}=600\,\mathrm{\,K\,}``
`` \,\mathrm{\,Using\,}\,\mathrm{\,the\,}\,\mathrm{\,equation\,}\,\mathrm{\,of\,}\,\mathrm{\,state\,}\,\mathrm{\,for\,}\,\mathrm{\,perfect\,}\,\mathrm{\,gas\,},\,\mathrm{\,we\,}\,\mathrm{\,get\,}``
`` PV=nRT``
`` \,\mathrm{\,For\,}\,\mathrm{\,the\,}\,\mathrm{\,vessel\,}\,\mathrm{\,of\,}\,\mathrm{\,volume\,}{V}_{\,\mathrm{\,o\,}}:``
`` {P}_{1}{V}_{o}=nR{T}_{1}...\left(1\right)``
`` \,\mathrm{\,For\,}\,\mathrm{\,the\,}\,\mathrm{\,vessel\,}\,\mathrm{\,of\,}\,\mathrm{\,volume\,}2{V}_{\,\mathrm{\,o\,}}:``
`` {P}_{2}\left(2{V}_{\,\mathrm{\,o\,}}\right)=nR{T}_{2}...\left(2\right)``
`` \,\mathrm{\,Dividing\,}\,\mathrm{\,eq\,}.\left(2\right)\,\mathrm{\,by\,}\,\mathrm{\,eq\,}.\left(1\right),\,\mathrm{\,we\,}\,\mathrm{\,get\,}``
`` \frac{2{P}_{2}}{{P}_{\mathit{1}}}=\frac{{T}_{\mathit{2}}}{{T}_{\mathit{1}}}=\frac{600}{300}=2``
`` \Rightarrow \frac{{P}_{\mathit{2}}}{{P}_{\mathit{1}}}=1``
`` \Rightarrow {P}_{\mathit{2}}\mathit{:}{P}_{\mathit{1}}=1:1``
`` ``
`` ``
`` ``