How much should the compressor generate?

[marellasunny]

Suppose the 2 passengers in my car generate 1000W of heat and the sunlight falling inside the car generates 1000W of heat, how much heat should my compressor add on the refrigerant to suck away all the 2000W of heat in the car?

I realize that a compressor is rated in pressure but I would like to know the thermodynamic equivalence.

Is the equation?

Heat generated inside car = Heat added to the refrigerant by the compressor

 

[maajdl]

Apparently that would be 2000 W times a kind of efficiency of your compressor.
But you would also need to account for heat losses through the envelope of the car.
The problem also is that the efficiency strongly depends on the external temperature.
It is not the same if you aspirate hot air or cold air from the outside.
It is not the same if the heat exchanger of the compressor sees an external temperature of 40°C or -10°C.

You can convert from compression factor to power assuming an adiabatic compression and some adiabatic efficiency. However, if the compressed gas reaches a temperature near the external cooling air temperature, you will have no way of cooling. Therefore, you understand that higher external temperatures will demand higher compression ratio.

______________________________
I hate cars and energy wasting too.

 

[russ_watters]

Passengers don't generate anywhere close to 1000W of heat, but regardless, the concept you are looking for is coefficient of performance (COP). A good air conditioner has a COP of 3 or 4, which means for every watt of mechanical energy input, it removes 3 or 4 watts of heat from the area being cooled.

 

[marellasunny]

Maajdl: Cleared-up the question I had.But,by efficiency,do you mean COP/the usual thermal efficiency ?

Russ_walters:COP does not have the variable Q_compressor(dot). How can I use COP to judge how much heat the compressor needs to generate to cool down 1000W?

 

[russ_watters]

The input for COP is compressor mechanical work. Since conservation of energy applies, all must be converted to heat.

...or are you asking about the heat separate from the temporary increase in fluid pressure energy? The compressor is probably on the order of 60% efficient so perhaps 60% is temporarily converted to presssure energy and the other 40% is immediately added as heat.