NOT WORTH POINTS PRACTICE EXAM$25$ pts $)$ Consider a Carnot power cycle $($i$.$e$.,$ Carnot heat engine$)$ where air is the working fluid. The start of the isothermal expansion process occurs at $10$ bar and $1500$ K and goes until the pressure is $1$ bar $.$ The isothermal compression process occurs at a temperature of $800$ K $.$

$($a$)(5$ pts$)$ Sketch the T$-$s diagram.

$($b$)(5$ pts$)$ Find the entropy change, in $k\frac{J}{k}g-K,$ during the isothermal expansion.

$($c$)(5$ pts$)$ Determine the $2$ theat input $(Q_H)$ in $k\frac{J}{k}g.$

$($d$)(5$ pts $)$ Determine the net work, in $k\frac{J}{k}g.$

$($e$)(5$ pts$)$ Determine the thermal efficiency.

You may assume a constant specific heat values $($given in Table on page $3$ of the exam$)...$although not needed depending on solution approach.

Hint: geometric arguments $($areas on the T$-$s diagram, based on the $"$TdS equations"$)$ are one approach to some sections of this problem; however, other methods will work too.