Not as simple as you suggest  Benyamin.

Real refrigerants do not obey the simple secondary school gas laws and they have a limited temperature range over which they can be used, because at some upper temperature compression no longer liquefies the gas, and equally at some lower limit, rarefaction will no longer cause evaporation, even at near vacuum.


In practice with '410 systems are run with the cold 'suction' side at  perhaps 50-100 PSI, and the hot compression side at a few hundred PSI. Much more or less than this and the  flow rates and rates of heat transport are not sensible with practical pipe sizes and pumps. This in turn tells you  the temperature limits for liquefaction and evaporation.  some info on R410A



The theoretical best is indeed that the heat transfer is in the ratio of the absolute temperatures - consider for an example  pumping between  300K (a rather toasty 23 degrees for indoors in the UK) from an outside temperature of 260 ( -13  which is  cold for an outside air temperature, but not incredibly cold for the cold parts of a heat pump working hard if it is air source against a frosty night.) the expected heat might be in the ratio 300/260 - so we put 40 watts in to suck 260 watts in from outside and push 300 into the room.  That would be a COP of 300/40, or about 7.
It is never that good, or indeed anything like that good. Half that would be very good.


In configurations  where the input icing up is a consideration ,the unit has to periodically reverse the heat flow to heat up and de-frost the outdoor unit, normally fans are stopped during this time, to avoid wafting cold air into the building and to stop sucking cold air over the frozen input heat exchanger. Sensing ice build up accurately, so as to neither perform unnecessary defrost cycles, nor to try and run with a frozen heat exchanger is an ongoing challenge. (i.e. there is as yet no 'one size fits all' reliable way)


There are plenty of good articles on the web, explaining various sources of non-ideality  Nordic heat pumps for example   .

Can I suggest that you may benefit from some background reading before commenting much further.

Not as simple as you suggest  Benyamin.

Real refrigerants do not obey the simple secondary school gas laws and they have a limited temperature range over which they can be used, because at some upper temperature compression no longer liquefies the gas, and equally at some lower limit, rarefaction will no longer cause evaporation, even at near vacuum.


In practice with '410 systems are run with the cold 'suction' side at  perhaps 50-100 PSI, and the hot compression side at a few hundred PSI. Much more or less than this and the  flow rates and rates of heat transport are not sensible with practical pipe sizes and pumps. This in turn tells you  the temperature limits for liquefaction and evaporation.  some info on R410A



The theoretical best is indeed that the heat transfer is in the ratio of the absolute temperatures - consider for an example  pumping between  300K (a rather toasty 23 degrees for indoors in the UK) from an outside temperature of 260 ( -13  which is  cold for an outside air temperature, but not incredibly cold for the cold parts of a heat pump working hard if it is air source against a frosty night.) the expected heat might be in the ratio 300/260 - so we put 40 watts in to suck 260 watts in from outside and push 300 into the room.  That would be a COP of 300/40, or about 7.
It is never that good, or indeed anything like that good. Half that would be very good.


In configurations  where the input icing up is a consideration ,the unit has to periodically reverse the heat flow to heat up and de-frost the outdoor unit, normally fans are stopped during this time, to avoid wafting cold air into the building and to stop sucking cold air over the frozen input heat exchanger. Sensing ice build up accurately, so as to neither perform unnecessary defrost cycles, nor to try and run with a frozen heat exchanger is an ongoing challenge. (i.e. there is as yet no 'one size fits all' reliable way)


There are plenty of good articles on the web, explaining various sources of non-ideality  Nordic heat pumps for example   .

Can I suggest that you may benefit from some background reading before commenting much further.