Question

Increasing the internal energy of a system ________ the Helmholtz free energy at constant TS.
(A) increases
(B) Decreases
(C) remains constant
(D) none of these

Answer 1

Hint: For this problem, we have to study the equation of Helmholtz free energy that is given by $A =$ $U - TS$ here, $A$ is considered as the Helmholtz free energy, $U$ is considered as the internal energy, $T$ is the temperature and $S$ is the enthalpy.

Complete step by step solution:
- In the given question, we have to explain that when the internal energy increases then what is the effect on Helmholtz free energy.
- As we know that the Helmholtz free energy is used to measure the work done by the system at constant temperature and volume.
- As we know that the Helmholtz free energy gives a relationship between internal energy, the temperature in Kelvin and enthalpy i.e.
$A =$ $U - TS$
- Here, $A$ is denoted by the Helmholtz free energy, $U$ represents internal energy, $T$ represents temperature and $S$ represents the enthalpy.
- Now, it is given in the question that TS is constant which it does not change under various conditions.
- So, when the internal energy will change, it will directly affect the Helmholtz free energy only.
- That's why when we increase the internal energy of the system, the Helmholtz free energy also increases and vice versa.

Therefore, option (A) is the correct answer.

Note: In the problem, the enthalpy tells us the amount of internal energy that is required to generate a system which is given by $H =$ $U + PV$ here, $U$ represents the internal energy and $P$ & $V$ represents the pressure and volume.