Two vessels A and B are connected via a stopc | vedclass

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(D) The process described is the free expansion of a gas into a vacuum.In free expansion,the external pressure $P_{	ext{ext}} = 0$.Since work done $w

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The pressure in vessel $B$ before opening the stopcock is zero.

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(D) The process described is the free expansion of a gas into a vacuum.In free expansion,the external pressure $P_{	ext{ext}} = 0$.Since work done $w = -P_{	ext{ext}} \Delta V$,it follows that $w = 0$.Because the system is in thermal equilibrium and the temperature remains constant,the internal energy change $\Delta U = 0$.According to the first law of thermodynamics,$\Delta U = q + w$,which implies $q = 0$.Therefore,the statement that the pressure in vessel $B$ before opening the stopcock is zero is the correct condition for free expansion.

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