Derive COP relations for the following internally reversible cycles. How does the COP

compare to the Carnot COP $($e$.$g$.,$ higher, lower, equal$)$ and why? Justify your answers

with thermodynamic considerations. You can consider either cooling or heating as target

application $(9$ points$)$

a$.$ Adiabatic and reversible compression & expansion, isothermal heat transfer $(3$

points$)$

b$.$ Adiabatic and reversible compression and expansion, linear temperature change

during heat addition and rejection $(3$ points$)$

c$.$ Isothermal compression and expansion, internal regeneration with $14=23,$

where q indicates the specific heat transfer $(3$ points$)$