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 th - Physics MCQ AIEEE 2004 2026 | ExamTest.live

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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:

A $T_{1} + T_{2}$
B $(T_{1} + T_{2}) /2$
C $\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}$
D $\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}$

Solution & Step-by-step Explanation

The vessels are insulated, so total internal energy is conserved. U_{1} + U_{2} = U_{t o t a l} \frac{f}{2} P_{1} V_{1} + \frac{f}{2} P_{2} V_{2} = \frac{f}{2} P (V_{1} + V_{2}) P = \frac{P _{1} V _{1} + P _{2} V _{2}}{V _{1} + V _{2}} Using ideal gas law n = \frac{P V}{RT} : n_{1} + n_{2} = n_{t o t a l} \frac{P _{1} V _{1}}{R T _{1}} + \frac{P _{2} V _{2}}{R T _{2}} = \frac{P ( V _{1} + V _{2} )}{RT} \frac{P _{1} V _{1}}{T _{1}} + \frac{P _{2} V _{2}}{T _{2}} = \frac{P _{1} V _{1} + P _{2} V _{2}}{T} T = \frac{P _{1} V _{1} + P _{2} V _{2}}{P _{1} V _{1} / T _{1} + P _{2} V _{2} / T _{2}} = \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}}

Try it yourself before checking the explanation above.

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:

T_{1} + T_{2}

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

\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}}

\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}

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