Two thermally insulated vessels 1 and 2 are filled with air at temperature $(T_{1}, T_{2})$ , volumes $(V_{1}, V_{2})$ and pressure $(P_{1}, P_{2})$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure)

T_{1} + T_{2}

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

(T_{1} + T_{2}) / 2

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

\frac{T_{1} T_{2} P (V_{1} + V_{2})}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}

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

\frac{T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2})}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}

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

Open in App

Solution

The correct option is C $\frac{T_{1} T_{2} P (V_{1} + V_{2})}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}$
From ideal gas law,
$P_{1} V_{1} = n_{1} R T_{1}$
$P_{2} V_{2} = n_{2} R T_{2}$
Since the total mass of the gas remains same before and after the vessels are joined,
$n_{1} + n_{2} = n$
$⟹ \frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}} = \frac{P (V_{1} + V_{2})}{R T}$
$⟹ T = \frac{T_{1} T_{2} P (V_{1} + V_{2})}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}$

Suggest Corrections

Similar questions

Two thermally insulated vessels $1$ and $2$ are filled with air at temperature ( $T_{1}$ , $T_{2}$ ), volume ( $V_{1}$ , $V_{2}$ ) and pressure ( $P_{1}$ , $P_{2}$ ) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $(T_{1}, T_{2})$ , volume $(V_{1}, V_{2})$ and pressure $(P_{1}, P_{2})$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be