Question

A system absorbs $10{\text{ kJ}}$ of heat and does $4{\text{ kJ}}$ of work. The internal energy of the system?
A. Increases by $6{\text{ kJ}}$
B. Decreases by $6{\text{ kJ}}$
C. Decreases by $14{\text{ kJ}}$
D. Increases by $14{\text{ kJ}}$

Answer 1

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.

Formula Used: $\Delta U = q + W$

Complete step by step solution:
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 $10{\text{ kJ}}$ for the heat, $4{\text{ kJ}}$ for the work done. Thus,
$\Delta U = \left( {10{\text{ kJ}}} \right) + \left( {4{\text{ kJ}}} \right)$
$\Delta U = 14{\text{ kJ}}$
Thus, the internal energy change of the system is $14{\text{ kJ}}$. The positive value of the internal energy indicates that the internal energy of the system increases.
Thus, the internal energy of the system increases by $14{\text{ kJ}}$.
Here, the system absorbs the heat. As heat is absorbed by the system, the reaction is endothermic. The positive value of the internal energy indicates that the work is done by the surrounding system.

**Thus, the correct option is (D) increases by $14{\text{ kJ}}$.

Note: **
If the system releases the heat then the reaction is an exothermic reaction. When the reaction is exothermic, the value of internal energy is negative. The negative value of the internal energy indicates that the work is done by the system on the surrounding and the internal energy of the system decreases.