The work done by a system is $8 \ J$,when $40 \ J$ heat is supplied to it. What is the increase in internal energy of the system in $J$?

The correct option for free expansion of an ideal gas under adiabatic condition is

If $\Delta H$ is the change in enthalpy and $\Delta E$ is the change in internal energy accompanying a gaseous reaction,which of the following is true?

Assuming all reactions occur in an open vessel,for which reaction will $\Delta H = \Delta U$?

Express the change in internal energy of a system when
$(i)$ No heat is absorbed by the system from the surroundings,but work $(w)$ is done on the system. What type of wall does the system have?
$(ii)$ No work is done on the system,but $q$ amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have?
$(iii)$ $w$ amount of work is done by the system and $q$ amount of heat is supplied to the system. What type of system would it be?

For the reaction $PCl_{5(g)} \to PCl_{3(g)} + Cl_{2(g)}$,which of the following relations is correct?