Chapter 10, Problem 5A

Interpretation Introduction

Interpretation :

The law of conservation of energy means that energy is a state function must be explained.

Concept Introduction :

Law of conservation of energy states that energy can’t be created or destroyed. It can be only interconverted to other form of energies.

A state function is the one which doesn’t depend on path in which the process is carried out rather it depends only on the initial and final state of the process.

Answer to Problem 5A

Energy is a state function as the change in energy change is independent of path.

Explanation of Solution

If a process is separately carried out in single step and multiple steps then in both the cases same amount of energy change will be involved provided the initial and final states are same.

Let’s consider a process is taking place from state A to state B and energy involved is E₁.

Now another multistep process is performed in which State A is converted to state C and then to state D and then to state E and then to state B. The energies for these processes are E₂, E₃, E₄ and E₅ respectively. Then as per state function requirement ${\text{E}}_{\text{1}}{\text{=E}}_{\text{2}}{\text{+E}}_{\text{3}}{\text{+E}}_{\text{4}}{\text{+E}}_{\text{5}}\text{.}$

Thus in these two processes there is no change in total energy. So it follows law of conservation of energy.

Conclusion

The law of conservation of energy means that energy is a state function. It is explained mathematically.