For isothermal expansion of an ideal gas into vacuum, among the following how many are zero 

$\Delta E,\Delta H,\Delta T,Q,P_{ext},\Delta S_{sys},\Delta S_{sur},\Delta S_{total},\Delta G_{sys}$

For isothermal (T = constant) expansion of an ideal gas into vacuum ; w = 0 since p_ex = 0. Also, Joule determined experimentally that q = 0; therefore, ∆U = 0

$\Delta E=\Delta H=\Delta T=q=p_{\alpha t}=\Delta S_{sur}=0$

$\Delta S_{sys}=\Delta S_{total}=+ve,\Delta G_{sys}-ve$