For questions $1a-1j,$ circle either True or False to indicate the validity of the statement.

$1$a$.$ True$/$False: The Clausius statement of the second law of thermodynamics asserts that: It is impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from a cooler to a hotter body.

$1$b$.$ True$/$False: For a closed system, it is impossible for a decrease in entropy to occur during an adiabatic process

$1$c$.$ True$/$False: Entropy production signifies a process is reversible.

$1$d$.$ True$/$False: The Clausius inequality cannot be applied to cycles.

$1$e$.$ True$/$False: The thermal efficiency of different reversible power cycles operating between the same two thermal reservoirs is always different.

$1$f$.$ True$/$False: A Carnot cycle is a reversible cycle consisting of four process that alternate between isentropic and isochoric.

$1$g$.$ True$/$False: An irreversible power cycle and a reversible power cycle are operating between the same two thermal energy reservoirs. It is possible for the irreversible cycle to output a larger magnitude of power than the reversible cycle.

$1$h$.$ True$/$False: It is impossible for an expansion valve to operate isentropically$.$ In other words, it is impossible for unrestrained expansion of a vapor$/$gas to occur reversibly.

$1$i$.$ True$/$False: The SI units for entropy are $k\frac{J}{K}$ and for specific entropy are $k\frac{J}{k}g-K$

$1$j$.$ True$/$False: A single thermal energy reservoir could serve as a heat source for once cycle and a heat sink for another.