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 .....

When a system is supplied with $60 \ J$ of heat,it performs $15 \ J$ of work. The change in the internal energy of the system is ......... $J$.

In a cylinder,$1.0 \, \text{kcal}$ of heat is added to $1.2 \, \text{L}$ of $O_2$ gas at a constant pressure of $1 \, \text{atm}$. The volume changes to $1.5 \, \text{L}$. Calculate the change in internal energy $(\Delta U)$ for this process. (in $, \text{kcal}$)

During the melting of an ice slab at $273 \ K$ and $1 \ atm$ pressure:

Three moles of an ideal gas expand reversibly under isothermal conditions from $2 \, L$ to $20 \, L$ at $300 \, K$. The amount of heat change (in $kJ / mol$) in the process is:

$4.0 \, L$ of an ideal gas is allowed to expand isothermally into vacuum until the total volume is $20 \, L$. The amount of heat absorbed in this expansion is $..... \, L \, atm$.