Systems and methods of heating and cooling cycle with isochoric heating

A system comprising:

• an apparatus configured to compress a refrigerant at a first state to a second state, the first state being at a first temperature and a first pressure, the second state being at a second temperature and a second pressure, the second temperature being higher than the first temperature, the refrigerant at the initial state being at a particular bulk density;
• cool the refrigerant at the second temperature and the second pressure to a third temperature, the second temperature being less than the third temperature, the cooling of the refrigerant being at a constant pressure;
• expand the refrigerant at the third temperature and the second pressure to a fourth temperature, the fourth temperature being less than the third temperature, the fourth temperature corresponding to a third state where the refrigerant is at the particular bulk density;
• and
• heat the refrigerant at the fourth temperature to the first temperature at the particular bulk density that is constant from the third state to the first state.

A method of a cooling cycle comprising:

• compressing a refrigerant at a first state to a second state, the first state being at a first temperature and a first pressure, the second state being at a second temperature and a second pressure, the second temperature being higher than the first temperature, the refrigerant at the initial state being at a first density;
• cooling the refrigerant at the second temperature and the second pressure to a third temperature, the second temperature being less than the third temperature, the cooling of the refrigerant being at a constant pressure;
• expanding the refrigerant at the third temperature and the second pressure to a fourth temperature, the fourth temperature being less than the third temperature, the fourth temperature corresponding to a third state where the refrigerant is at the particular bulk density;
• heating the refrigerant at the fourth temperature to a fifth temperature at a particular bulk density that is constant from the third state to a fourth state using isochoric heating;
• and
• heating the refrigerant from the fourth state to the first state using isobaric vaporization.