Two identical blocks of constant heat capacity $C$ at $400 K$ and $200 K$ are brought to thermal equilibrium. Which statements are correct?

AIf they are placed in direct contact (isolated from the rest), the final temperature is $300 K$ .
BFor direct contact, $Δ S_{t o t a l} = 0$ .
CIf a reversible engine is run between them until they reach equal temperatures, the final temperature is about $282.8 K$ .
DIn the reversible-engine case, $Δ S_{t o t a l} > 0$ .

Answer: A, C

Direct contact:

T_{f} = 300 K

(true) and

Δ S = C ln (300/400) + C ln (300/200) = C ln 1.125 > 0

(B false). Reversible engine:

Δ S_{t o t a l} = 0

, so

C ln (T_{f} /400) + C ln (T_{f} /200) = 0

T_{f} = 400 \times 200 = 282.8 K

(C true, D false). The engine also delivers work

C (600 - 2 T_{f}) > 0