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A vessel of volume 3V contains a gas at ...

A vessel of volume `3V` contains a gas at pressure `4 P_(0)` and another vessel of volume `2V` contains same gas at pressure `1.5 P_(0)`. Both vessels have same temperature. When both vessels are connected by a tube of negligible volume, the equilibrium is `IP_(0)`, where `I` is an integer. Find the value of `I`.

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The correct Answer is:
3
No change of temperature
So `(n_1 + n_2)_i = (n_1 + n_2 )f," "(P_1 V_1)/(RT) + (P_2 V_2)/(RT) = (PV_1)/(RT) + (PV_2)/(RT)`
So `P = (P_1 V_1 + P_2 V_2)/(V_1 + V_2)" ="((4P_0)(3V)+(1.5P_0)(2V))/(5V)`
`= 3P_0 = IP_0` (given) So l = 3
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