For the exothermic reaction of $1 \ mol$ of $Zn$ dust with $1 \ mol$ of $H_2SO_4$ in a bomb calorimeter,the relationship between $\Delta U$ and $w$ is .....

$A$ mixture of $2 \ mol$ of carbon monoxide and $1 \ mol$ of oxygen in a closed vessel is ignited to convert the carbon monoxide to carbon dioxide. If $\Delta H$ is the enthalpy change and $\Delta E$ is the change in internal energy,then:

At a certain temperature, $T(K)$, during a process, $500 \text{ J}$ is absorbed by the system and work of $200 \text{ J}$ is done by the system. Then the change in internal energy of the system is: (in $\text{ J}$)

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?

Five moles of an ideal gas at $293 \, K$ is expanded isothermally from an initial pressure of $2.1 \, MPa$ to $1.3 \, MPa$ against a constant external pressure of $4.3 \, MPa$. The heat transferred in this process is $...... \, kJ \, mol^{-1}$. (Rounded-off to the nearest integer) $\left[\right.$ Use $R = 8.314 \, J \, mol^{-1} \, K^{-1}\left.\right]$

What is the change in internal energy if a system gains $x \ J$ of heat and $y \ J$ of work is done on it?