Six kilograms of carbon dioxide in a piston-cylinder device execute a Carnot cycle consisting of the following four processes.
Process 1-2: Adiabatic compression
Process 2-3: Isothermal heat addition
Process 3-4: Adiabatic expansion
Process 4-1: Isothermal heat rejection
The minimum and maximum gas temperatures are 300 K and 900 K, respectively. The heat transfer to the gas during the isothermal expansion is 1200 kJ. At the end of the isothermal expansion the pressure is 800 kPa (State 3). After adiabatic expansion of the gas, the pressure decreases to 14.73 kPa (State 4). Consider variable specific heats for carbon dioxide.
(a) Determine the pressure (kPa) at the start and end of adiabatic compression.
(b) Find the volume (m3) of at the start and end of isothermal heat rejection.
(c) Calculate work (kJ) and heat transfer (kJ) for each process in the cycle.
(d) Calculate the thermal efficiency (%) of the cycle using work and heat transfer. Check that the value matches the Carnot efficiency.
(e) Show the cycle on P-V diagram.