Homework problem 9.47

[Tasnia Haider 1E]

In 9.47, the question asks about an isothermal, irreversible, free expansion. How do we know that the change in internal energy is zero from this phrase? Since internal energy is zero, that means q is also zero.

[Danah Albaaj 1I]

In Chapter 8, we are given the equation ∆U=3/2nR∆T to relate the change in internal energy to the change in temperature. If a system is isothermal, this means that ∆U=0 for this system. Using the first law of thermodynamics, we can determine the q=-w, rather than 0 .

[Rachel Formaker 1E]

Isothermal means that the temperature does not change in the reaction. For all isothermal reactions, there is no change in internal energy, so ΔU=0.
In this problem, we are told that ΔU=0 because the reaction is isothermal. Since no work is done in free expansion (w=0) and ΔU = q + w, when ΔU=0 and w=0, q must also be 0.