One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27\,^{\circ}C$. If the work done during the process is $3\, kJ$,then the final temperature of the gas is $(C_v = 20\, J/K)$ .....$K$

The work done by the system is $8 \, J$. When $40 \, J$ of heat is supplied to the system,the change in internal energy of the system during the process is ...... $J$.

Calculate the change in internal energy of the system if $20 \ kJ$ of work is done on the system and it releases $10 \ kJ$ of heat in a particular reaction. (in $kJ$)

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

Assertion : For a reaction $2NH_{3(g)} \to N_{2(g)} + 3H_{2(g)}$ ; $\Delta H > \Delta E$.
Reason : Enthalpy change is always greater than internal energy change.

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?