Consider a Carnot engine operating steadily using ideal gas, $100-g$ hydrogen, as the working

fluid. The work output is measured to be one third of the heat input to this engine. During

the heat addition process, the temperature of hydrogen is $250C$ and the entropy of hydrogen

increases by $3k\frac{J}{K}.$

$($a$)$ Calculate the thermal efficiency of this heat engine.

$($b$)$ Calculate the temperature at which the hydrogen rejects heat.

$($c$)$ Calculate the amount of heat in kJ the hydrogen rejects per cycle.

$($d$)$ If the volume expands tenfold in the reversible isothermal expansion process, calculate

the work interaction during this process per cycle.

$($e$)$ Graph the process path of $100-g$ hydrogen going through the Carnot cycle on a temperature$-$

entropy $(T-S)$ diagram.

Now, the $100-$g hydrogen is placed into a piston$-$cylinder device with negligible friction

between the piston head and the cylinder wall.

$($f$)$ The pressure of hydrogen is maintained as a constant at $150$ kPa $.$ The initial temper$-$

ature of hydrogen is $300$ K $.$ A resistance heater within the cylinder is turned on and

passed a current of $0\mathrm{.}2$ A for $8$ min from a $120-V$ power source. At the same time, a

heat loss of $4\mathrm{.}52$ kJ occurs. Determine the final temperature of hydrogen.

$($g$)$ Graph the process path of $100-g$ hydrogen going through this constant$-$pressure process

on a temperature$-$volume $(T-V)$ diagram. If it is a straight line, indicate its slope.