Question

If $20{\text{ kJ}}$ work is done by water and $30{\text{ kJ}}$ heat was lost, the internal energy change of water is
A.$ - 5{\text{ kJ}}$
B.$ - 50{\text{ kJ}}$
C.$ - 10{\text{ kJ}}$
D.$ + 50{\text{ kJ}}$

Answer 1

Hint:Here, the work is done by the water i.e. work is done by the system on the surrounding. And heat is lost i.e. the reaction is exothermic.

Complete step by step answer:
The work is done by water. Thus, work is done by the system on the surrounding. Thus, the sign of work done is negative.
Thus, the work done is $ - 20{\text{ kJ}}$.
The heat is lost in the reaction. Thus, the reaction is exothermic. Thus, the sign for the heat lost is negative.
Thus, the heat lost is $ - 30{\text{ kJ}}$.
Calculate the internal energy change using the equation as follows:
$\Delta U = q + W$
Where, $\Delta U$ is the internal energy change,
$q$ is the heat,
$W$ is the work done.
Substitute $ - 30{\text{ kJ}}$ for the heat, $ - 20{\text{ kJ}}$ for the work done. Thus,
$\Delta U = \left( { - 30{\text{ kJ}}} \right) + \left( { - 20{\text{ kJ}}} \right)$
$\Delta U = - 50{\text{ kJ}}$
Thus, the internal energy change is $ - 50{\text{ kJ}}$.
Thus, If $20{\text{ kJ}}$ work is done by water and $30{\text{ kJ}}$ heat was lost, the internal energy change of water is $ - 50{\text{ kJ}}$.
Thus, the correct option is option (2).

Note:
The energy of a system that arises due to the molecular state of motion of matter is known as the internal energy of the system. As the temperature increases the phase of the matter changes from solid to liquid or from liquid to gas and thus, the internal energy increases. Internal energy is an extensive property of a system i.e. it depends on the mass of the system and it is a state function. Internal energy is denoted by symbol U.