Two vessels A and B are connected via stopcock. Vessel A is filled with a gas at a certain pressure. The entire…

🧠 Free expansion into vacuum: $w = 0$, $q = 0$, $\Delta U = 0$ — so vessel B must have been evacuated No temperature change means $\Delta U = 0$ for an ideal gas (internal energy depends only on temperature). Since no work is done ($P_{\text{ext}} = 0$) and no heat flows, the only consistent interpretation is that vessel B had zero initial pressure.

Evaluating options:

• (a) $dw \neq 0$: False — expansion into vacuum does no work.
• (b) $dq \neq 0$: False — $Delta U = 0$ and $w = 0$ forces $q = 0$.
• (c) $dU \neq 0$: False — temperature is unchanged so $\Delta U = 0$.
• (d) Pressure in B before opening was zero: True — this is the definition of free expansion.

$\boxed{\text{Answer: (d)}}$