Question

Two closed vessels of equal volume contain air at pressure $100\text{kPa}$ and temperature $250\text{K}$ and are connected through a narrow tube. If one of the vessels is now maintained at $250\text{K}$ and the other at $300\text{K}$, what will be the pressure in the vessels?

• A. $100\text{kPa}$
• B. $210\text{kPa}$
• C. $109\text{kPa}$
• D. $120\text{kPa}$

Answer 1

The correct option is C $109\text{kPa}$

Let the initial pressure, volume and temperature in each vessel be $P_0(=100\text{kPa}),V_0$ and $T_0(=250\text{K})$. Let the number of moles in each vessel be $n$.


At final state, both vessels have same pressure $P$ and let the number of moles be $n_1,n_2$ respectively .
Then, $n_1+n_2=2n$ [Total moles will be same]
Using ideal gas equation,
$\frac{P{V}_0}{R{T}_0}+\frac{P{V}_0}{R{T}_1}=2\frac{P_0{V}_0}{R{T}_0}$
$\Rightarrow \frac{P}{T_0}+\frac{P}{T_1}=\frac{2P_0}{T_0}$
$\Rightarrow P=\frac{2P_0}{T_0}\times \frac{T_0\times T_1}{T_0+T_1}$
$=\frac{2\times 100}{250}\times \frac{250\times 300}{550}$
$\therefore P=109\text{kPa}$