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An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume `V_1` and contains ideal gas at pressure `P_1` and temperature `T_1`.The other chamber has volume `V_2` and contains ideal gas at pressure `P_2` and temperature `T_2`. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will beA. `(T_(1)T_(2)(P_(1)V_(1) + P_(2)V_(2)))/(P_(1)V_(1)T_(2) + P_(2)V_(2)T_(1))`B. `(P_(1)V_(1)T_(1) + P_(2)V_(2)T_(2))/(P_(1)V_(1) + P_(2)V_(2))`C. `(P_(1)V_(1)T_(2) + P_(2)V_(2)T_(1))/(P_(1)V_(1) + P_(2)V_(2))`D. `(T_(1)T_(2)(P_(1)V_(1) + P_(2)V_(2)))/(P_(1)V_(1)T_(1) + P_(2)V_(2)T_(2))` |
Answer» Correct Answer - A `U = U_(1) + U_(2) implies (n_(1) + n_(2)) C_(V)T = n_(1)C_(V)T_(1)+ n_(2)C_(V)T_(2)` `implies T = ((P_(1)V_(1) + P_(2)V_(2)) T_(1)T_(2))/((P_(1)V_(1)T_(2) + P_(2)V_(2)T_(2)))` |
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