A large vacuum chamber of volume ' V ' is connected to a narrow cylindrical pipe which is initially filled with an ideal diatomic gas at temperature T 0 , pressure P 0 volume V 0 ( ≪ V

Question

A large vacuum chamber of volume ' V ' is connected to a narrow cylindrical pipe which is initially filled with an ideal diatomic gas at temperature $T_{0}$ , pressure $P_{0}$ volume $V_{0} (≪ V)$ . The gas is enclosed by a light insulating piston and the air outside is constant pressure $P_{0}$ . Now the gas in the pipe slowly allowed to leak into the vacuum chamber through a small opening as shown. All the walls are insulated. The final pressure ' P ' and the temperature ' T ' of the gas are given by

TestHub · Accepted Answer

Wg = Work done against surrounding = − P 0 ​ V 0 ​ as veseel walls are adiabatic, Q = 0 , Δ U = − W ⇒ nC v ​ Δ T = P 0 ​ V 0 ​ r − 1 n R ⋅ Δ T ​ = P 0 ​ V 0 ​ ⇒ Δ T = ( r − 1 ) T 0 ​ ⇒ T − T 0 ​ = ( r − 1 ) T 0 ​ T = r T 0 ​

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