Problem 1 (10 points). Consider a newly invented power cyclic device performing a power
cycle while interacting with two thermal reservoirs. The device absorbs 2000 kJ from the
hight temperature reservoir at 1000 K, and releases certain amount of heat to the low
temperature reservoir at 500 K. Now consider three claims on its thermal efficiency or per-
formance: $\eta$=60%, $\eta$=50%, and $\eta$=40%.
(a, 4 points) Formulate the entropy production for the cyclic process in terms of the given
parameters: temperatures of the reservoirs, thermal efficiency, and heat transfer from high
temperature reservoir.
(b, 2 points) Find the entropy production for the case $\eta$=60%, justify the possibility of
this invention, and determine whether this is a reversible or irreversible power cycle.
(c, 2 points) Find the entropy production for the case $\eta$=50%, justify the possibility of
this invention, and determine whether this is a reversible or irreversible power cycle.
(d, 2 points) Find the entropy production for the case $\eta$=40%, justify the possibility of
this invention, and determine whether this is a reversible or irreversible power cycle.
Hint: Clausius inequality, T.D. 1st and 2nd laws.
