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?

(N/A) The first law of thermodynamics states that $\Delta U = q + w$.
$(i)$ Since no heat is absorbed,$q = 0$. Therefore,$\Delta U = w$. The system has an adiabatic wall.
$(ii)$ Since no work is done,$w = 0$. Heat is taken out,so $q$ is negative. Therefore,$\Delta U = -q$. The system has thermally conducting walls (diathermal walls).
$(iii)$ Work is done by the system,so $w$ is negative. Heat is supplied to the system,so $q$ is positive. Therefore,$\Delta U = q - w$. This describes a closed system.