Give the mathematical expression for the first law of thermodynamics.

When a system expands under adiabatic conditions,what happens to its internal energy?

Find the approximate value of $(\Delta H - \Delta U)$ in $J \cdot mol^{-1}$,for the formation of $CO$ from its elements at $298 \ K$. $(R = 8.314 \ J \cdot K^{-1} \ mol^{-1})$

$A$ piston filled with $0.04\, mol$ of an ideal gas expands reversibly from $50.0\, mL$ to $375\, mL$ at a constant temperature of $37\, ^oC$. It absorbs $208\, J$ of heat in this process. The value of $q$ and $w$ for the process will be: $(R = 8.314\, J / mol\, K)$ $(\ln 7.5 = 2.01)$

When $1 \ mole$ of gas is heated at constant volume,the temperature rises from $273 \ K$ to $546 \ K$. If heat supplied to the gas is $x \ J$,then find the correct statement from the following.

Two moles of an ideal monoatomic gas are allowed to expand adiabatically and reversibly from $300 \ K$ to $200 \ K$. The work done in the system is $... \ kJ$ $(C_V = 12.5 \ J/K/mol)$.