Suppose That an Object's Entropy Increases from Zero When Its $U=0$

Multiple Choice

Suppose that an object's entropy increases from zero when its thermal energy is $U=0$ to some maximum value when $U=\frac{1}{2} U_{\text {max }}$ , and then goes back to zero when $U=U_{\max }$ (as shown in the drawing below) . The greatest thermal energy $U$ that such an object could have when in thermal equilibrium with a normal object is closest to which of the following?

A) 0
B) $\frac{1}{4} U_{\max }$
C) $\frac{1}{2} U_{\max }$
D) $\frac{3}{4} U_{\max }$
E) $U_{\max }$
F) Other (specify)