Question

In a reaction 2.5kJ of heat is released from the system and 5.5kJ of work is done on the system. Calculate $\Delta U$.

Answer 1

In the above reaction, amount of heat released and amount of work done is given. So, using the first law of thermodynamics we can determine the $\Delta U$. The first law of thermodynamics will provide the relationship of internal energy, heat and work done.

Complete answer:
What does the first law of thermodynamics explain? The first law of thermodynamics says that when heat or energy moves inside or outside the system, then the internal energy of the system also changes accordingly. The first law of thermodynamics is based on the law of conservation of energy. It says that energy can neither be created nor be destroyed, but can be transformed from one into another. Similarly, heat cannot be lost. But it can be exchanged between the system and the surroundings.
This is given by an equation:
$\Delta U = q + w$
Where,
$\Delta U$=internal energy change
$q$=transfer of heat between system and surrounding
$w$=work done on or by the system
In this reaction, $\Delta U = q + w$:
q is positive when the heat is absorbed by the system.
q is negative when the heat is released from the system.
Similarly, we can say that
w is positive when the work is done by the system.
w is negative when the work is done on the system.
In the given problem, it has given that heat released is 2.5kJ and work done on the system is 5.5kJ.
As energy is being released, q=-ve and work is done on the system, therefore w=-ve.
$\Delta U = q + w$
$\Delta U = - 2.5kJ - 5.5kJ$
$\Delta U = - 8.0kJ$

The internal energy of the system is $\Delta U = - 8.0kJ$.

Additional information:
- Endothermic reaction:
The chemical reaction in which the heat energy is absorbed by the reactants, from the surrounding to form products such a type of reaction is called endothermic reaction.
- Exothermic reaction:
The chemical reaction in which the heat energy is released in the form of heat by the system into the surrounding, then such type of reaction is called exothermic reaction.

Note: Always remember that when the heat is released then ‘q’ will be negative and when heat is absorbed then ‘q’ will be positive. When the work is done on the system, then ‘w’ will be negative and When the work is done by the system, then ‘w’ will be positive.