# Carnot COP of Brine-water Heatpump

The maximum reachable efficiency for a heat pump can be calculated using Lorenz/Carnot cycle:

$$COP = \frac{T_H}{T_H - T_C}$$

Where as the $$T_H$$ is the target temperature and $$T_C$$ is the reservoir temperature (I might be wrong about the exact terminology).

In case of heating houses with brine-water the temperature of brine can exceed 50°C where as the target temperature is max 25°C.

1. How does the formula translate for this scenario, is it even considered heating?
2. If its not considered heating, would it be logical to step up the brine temperature and store the energy in containers for house use?
3. What is the typical method of incorporating heat pumps with high temperature brine-water sources?
• 50 degree C brine would be geothermal heating. You don't need a heat pump to move heat from cold to hot, just a heat exchanger Commented Jan 15 at 13:59
• @TigerGuy "Move heat from cold to hot" needs work... Moving heat from Hot to Cold does not. Commented Jan 15 at 14:12
• @SolarMike, yes, I got it backwards Commented Jan 15 at 19:19
• @TigerGuy considering we want to achieve certain Co2/kWh of output heat, (Co2 for electricity generation), how would this formula change? is it a better way to calcualte Heatpump efficiency using thermodynamics ?
– Ali
Commented Jan 16 at 9:00
• Is the heat to be transferred direct from the hot brine to the indoor air, or is there a secondary water loop/system involved? In the former case, @TigerGuy's comment applies, but you have to worry about how you're going to get hot tap water hot enough for all the hygiene purposes one wants hot tap water to serve. In the latter case, a heat pump might indeed be useful. Commented Jan 16 at 13:54