NEET-XII-Physics
24: Kinetic Theory of Gases
- #26Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.Ans : `` \begin{array}{l}\text{Here,}\\ {P}_{1}=2\times {10}^{5}pa\\ {V}_{1}=0.002{\text{m}}^{\text{3}}\\ {V}_{2}=0.0005{m}^{3}\\ {T}_{1}={T}_{2}=300K\\ \\ \,\mathrm{\,Number\; of\; moles\; initially\,},{n}_{1}=\frac{{P}_{1}{V}_{1}}{R{T}_{1}}\\ \Rightarrow {n}_{1}=\frac{2\times {10}^{5}\times 0.002}{8.3\times 300}\\ \Rightarrow {n}_{1}=0.16\\ \text{Applying equation of state, we get}\\ {P}_{2}{V}_{2}={n}_{2}RT\\ \text{Assuming the final pressure becomes equal to the atmospheric pressure, we get}\\ {P}_{2}=1.0\times {10}^{5}pa\\ \Rightarrow {n}_{2}=\frac{{P}_{2}{V}_{2}}{RT}\\ \Rightarrow {n}_{2}=\frac{1.0\times {10}^{5}\times 0.0005}{8.3\times 300}\\ \Rightarrow {n}_{2}=0.02\\ \text{Number of leaked moles =}{n}_{2}-{n}_{1}\\ =0.16-0.02\\ =0.14\end{array}``
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