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An ideal gas is kept in two adjacent chambers of volume $v$ and $2 v$ . separated by a thin partition, under initial conditions as shown in figure. The chamber is adiabatic ie no heat flows in or out. Now the partition is removed and the gas is allowed to stabilize. If $P_{f}$ and $T_{f}$ are the values of final pressure and temperature then -
Option: 1
$P_{f}=\frac{5}{3} P$

Option: 2
$P_{f}=P$

Option: 3
$\frac{P_{p}}{T_{f}}=\frac{8}{q} \frac{P}{T}$

Option: 4
$T_{f}=\frac{3}{8} T$

Answers (1)

best_answer

Referring as $x$ and $y$ for chambers (I) and (II)

$\begin{aligned} n_{x} & =\frac{P_{x} V_{x}}{R T_{x}} \quad n_{y}=\frac{P_{y} V_{y}}{R T_{y}} \\ & \Rightarrow P_{f}=\frac{R T_{f}}{V_{f}}\left(n_{x}+n_{y}\right) \end{aligned}$

Substitute for $n_{x}$, $n_{y}$

$\begin{aligned} \frac{P_{f}}{T_{f}} & =\frac{R}{V_{f}}\left(\frac{P_{x} V_{x}}{R T_{x}}+\frac{P_{x} V_{y}}{R T_{y}}\right) \\ & =\frac{1}{3 V}\left(\frac{2 P v}{T}+\frac{2 P V}{3 T}\right) \\ & =\frac{2 P}{3}\left(\frac{1}{T}+\frac{1}{3 T}\right) \\ & \Rightarrow \frac{P_{f}}{T_{f}}=\frac{8 P}{9 T} \end{aligned}$

Posted by

Gautam harsolia

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