When we analyze the equation [tex]\(\Delta H = \Delta U + V \Delta p\)[/tex], we are looking at the relationship between the change in enthalpy ([tex]\(\Delta H\)[/tex]), the change in internal energy ([tex]\(\Delta U\)[/tex]), and the product of volume ([tex]\(V\)[/tex]) with the change in pressure ([tex]\(\Delta p\)[/tex]).
Given the context of the problem where the change in pressure ([tex]\(\Delta p\)[/tex]) is very small, let's examine the implications:
1. Consider the term [tex]\(V \Delta p\)[/tex]:
- When [tex]\(\Delta p\)[/tex] is very small, the product [tex]\(V \Delta p\)[/tex] becomes negligible because we are multiplying the volume by a very small number.
2. Implications on [tex]\(\Delta H = \Delta U + V \Delta p\)[/tex]:
- With [tex]\(V \Delta p\)[/tex] being so small, it approaches zero. Thus, the term [tex]\(V \Delta p\)[/tex] has very little effect on the overall equation.
3. Simplification:
- Since [tex]\(V \Delta p\)[/tex] is negligible, we can simplify the equation to:
[tex]\[
\Delta H \approx \Delta U
\][/tex]
This means that when the change in pressure ([tex]\(\Delta p\)[/tex]) is very small, the equation [tex]\(\Delta H = \Delta U + V \Delta p\)[/tex] simplifies to [tex]\(\Delta H \approx \Delta U\)[/tex].
So, the correct option is:
b) Then, [tex]\(\Delta U \gg V \Delta p\)[/tex], so we can assume [tex]\(\Delta H = \Delta U\)[/tex].
