What is meant by standard state in the context of the equation $\Delta U = q + w$?

The internal energy of a substance $U$ is related to temperature $T$ in which of the following ways?

Consider the expansion given in problem $6.2$,for $1 \, mol$ of an ideal gas conducted reversibly.

What is the work done when a gas is compressed from $2.5 \times 10^{-2} \ m^3$ to $1.3 \times 10^{-2} \ m^3$ at a constant external pressure of $4.05 \ bar$ (in $J$)?

Three moles of an ideal gas expanded spontaneously into vacuum. The work done will be .............. $Joules$.

What is the work done when $2 \text{ mole}$ of an ideal gas are expanded isothermally and reversibly from $5 \text{ m}^{3}$ to $10 \text{ m}^{3}$ at $300 \text{ K}$ (in $\text{ kJ}$)? $(R=8.314 \text{ J K}^{-1} \text{ mol}^{-1})$