Two closed bulbs of equal volume $(V)$ containing an ideal gas initially at pressure $p_{i}$ and temperature $T_{1}$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_{2}$ . The final pressure $p_{f}$ is :

p_{i} (\frac{T_{1} T_{2}}{T_{1} + T_{2}})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 p_{i} (\frac{T_{1}}{T_{1} + T_{2}})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 p_{i} (\frac{T_{2}}{T_{1} + T_{2}})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 p_{i} (\frac{T_{1} T_{2}}{T_{1} + T_{2}})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2 p_{i} (\frac{T_{2}}{T_{1} + T_{2}})$
Initially, number of moles of gas in each bulb is $n_{1} = \frac{p_{i} V}{R T_{1}}$ and $n_{2} = \frac{p_{i} V}{R T_{1}}$

After the temperature of second bulb is raised to $T_{2}$ then the number of moles of gas in both the bulbs are :

$n_{1}^{'} = \frac{p_{f} V}{R T_{1}}$ and $n_{2}^{'} = \frac{p_{f} V}{R T_{2}}$

Now, the total number of moles of gas in both the bulbs remains same in both the cases.

$n_{1} + n_{2} = n_{1}^{'} + n_{2}^{'}$

$\frac{2 p_{i} V}{R T_{1}} = \frac{p_{f} V}{R T_{1}} + \frac{p_{f} V}{R T_{2}} \Rightarrow \frac{2 p_{i} V}{R T_{1}} = \frac{p_{f} V}{R} (\frac{T_{2} + T_{1}}{T_{1} T_{2}})$

$p_{f} = \frac{2 p_{i} T_{2}}{T_{1} + T_{2}}$ .

Therefore, the correct option is C.

Suggest Corrections

Similar questions

Q. Two closed bulbs of equal volume

(V)

containing an ideal gas initially at pressure

P_{i}

and temperature

T_{1}

are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to

T_{2}

. The final pressure

p_{f}

is :

Q. Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure

p_{1}

and temperature

T_{1}

are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to

T_{2}

. The final pressure

p_{f}

is:

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $p_{i}$ and temperature $T_{1}$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_{2}$ .The final pressure $p_{f}$ is: