Two flasks I and II shown below are connected by a valve of negligible volume.
When the valve is opened, the final pressure of the system in bar is x × 10-2. The value of x is ______. (Integer answer)
[Assume Ideal gas; 1 bar = 105 Pa; Molar mass of N2 = 28.0 g mol-1 ; R = 8.31 J mol-1 K-1]
Applying ; (nI + nII)initial = (nI + nII)final
⇒ Assuming the system attains a final temperature of T (such that 300 < T < 60)
⇒ \(\Big(Heat\; lost \; by \; N_2 \\ of \; container I \Big)\) = \(\Big(Heat\; gained \; by \; N_2 \\of \; container II \Big)\)
⇒ nI Cm (300–T) = nII Cm (T–60)
⇒ \(\Big(\frac{2.8}{2.8}\Big)\)(300 - T) = \(\frac{0.2}{28}\)(T - 60)
⇒ 14(300 – T) = T – 60
⇒ \(\frac{14 \times 300 + 60}{15}\) = T
⇒ T = 284 K (final temperature)
⇒ If the final pressure = P
⇒ (nI + nII)final = \(\Big(\frac{3.0}{2.8}\Big)\)
⇒ \(\Big(\frac{P}{RT}\Big)\)(VI + VII) = \(\frac{3.0\;gm}{28\;gm/mol}\)
P = \(\Big(\frac{3}{28}\Big)\)mol x 8.31 \(\frac{J}{mol-K}\) x \(\frac{284 K}{3 \times 10^{-3}m^3}\)x \(10^{-5}\frac{bar}{Pa}\)
⇒ 0.84287 bar
⇒ 84.28 x 10-2 bar
⇒ 84