First slide

Introduction-thermodynamics

Question

In a toy truck the volume of tube is 2000 cc in which air is filed at a pressure $2 \times 10^{5} N / m^{2}$ . When the tube gets punctured, its volume reduces to 500 cc. Find the number of moles of air leaked out in the puncture. Take atmospheric pressure is 10⁵ N/m² and atmospheric temperature 27°C.

Moderate

Solution

Initial moles of air tube are
$x_{i} = \frac{P_{i} V_{i}}{{RT}_{i}} = \frac{2 \times 10^{5} \times 2000 \times 10^{- 6}}{8 .314 \times 300} = 0 .16$
final moles of air in tube after puncture are
$n_{f} = \frac{P_{f} V_{f}}{{RT}_{f}} = \frac{10^{5} \times 500 \times 10^{- 6}}{8 .314 \times 300} = 0 .02$
moles leaked out from tube $Δn = n_{i} - n_{f} = 0 .16 - 0 .02 = 0 .14 mol$

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