Question

a system gains 782 kj of heat, resulting in a change in internal energy of the system equal to +186 kj. how much work is done?

was work done on the system or by the system?
work was done on the system.
work was done by the system.

Explanation:

Step1: Recall the first law of thermodynamics

The first law of thermodynamics is given by $\Delta U=q + w$, where $\Delta U$ is the change in internal energy, $q$ is the heat added to the system, and $w$ is the work done.
Given that $q = 782\ \text{kJ}$ and $\Delta U=186\ \text{kJ}$.
We need to solve for $w$.

Step2: Rearrange the formula to solve for $w$

Rearrange $\Delta U=q + w$ to get $w=\Delta U - q$.
Substitute the values: $w = 186\ \text{kJ}-782\ \text{kJ}$.

Step3: Calculate the value of $w$

$w=-596\ \text{kJ}$

Since $w=- 596\ \text{kJ}$ (negative value), according to the sign convention ($w>0$ when work is done on the system and $w < 0$ when work is done by the system), work is done by the system.

Answer:

$w=-596\ \text{kJ}$; Work was done by the system.