Two identical vessels are connected by a tube. Volume of the tube is vanishingly small and it is equipped with a valve
One of the vessels contains nitrogen at pressure
P1 and temperature T, and the other vessel contains oxygen at pressure P2 and temperature T2. The system is well
insulated from the surroundings. Now the valve is
opened. The final pressure P and temperature T are attained by mixture of both the gases. Then (Assuming gases to be
ideal and non-interactive)
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