Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature T. It is allowed to rush freely into the right chamber of volume V which is initially vacuum. The whole system is thermally isolated. What will be the final temperature of the system after the equilibrium has been attained?

Consider the given diagram. An ideal gas is contained in a chamber (le

1.	Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature T. It is allowed to rush freely into the right chamber of volume V which is initially vacuum. The whole system is thermally isolated. What will be the final temperature of the system after the equilibrium has been attained?
Answer» `T ` `T/2` `2T` `T/4` Solution :From the ideal gas equation , `PV = nRT `, we GET initially , `P_(i) V_(i) = n RT_(i)` and after the gas is allowed to rush freely into the right chamber, then `P_(f)V_(f) = nRT_(f)` Now , given , `P_(i) = P , V_(i) = V , P_(f) = P//2 , V_(f) = 2V, T_(i) = TP_(i) V_(i) = nRT rArr PV = nRT ` Now , `P_(f) V_(f) = n RT_(f) rArrP/2 xx 2V = nRT_(f)` `rArr PV = nRT_(f) rArr nRT = nRT_(f)` ` rArrT_(f) = T ` ` :. ` Initial and final TEMPERATURE of the system remains same after the equilibrium has been attained as the system is not doing any work at the time of free expansion `(i.e., Delta U = 0 )`.

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