w_max & T in fuel cell

eraemia

1. The problem statement, all variables and given/known data

2 H2(g) + O2(g) 2 H2O(l) K = 1.28e83

As temperature increases, does the maximum amount of work obtained from the fuel cell reaction increase, decrease, or remain the same?

2. Relevant equations

1. G = -RTln(K)
2. dG = dH - tdS
3. w_max = dG

3. The attempt at a solution

Okay, using formation values, I calculated that for this reaction, both dH and dS are < 0.

If dG = w_max (eq. 3), then w_max = -RT ln K (1 and 3)
Since ln(K) is positive, the larger the T, the more negative w_max.
Thus, as T increases, w_work decreases?

Is that right? Thanks.