Question

If the efficiency of a power plant goes up as the low temperature drops why not let the heat rejection go to a refrigerator at say –10°C instead of ambient 20°C?

Answer 1

The refrigerator must pump the heat up to 20°C to ** it to the ambient. The refrigerator must then have a work input that will exactly offset the increased work output of the power plant, if they are both ideal. As we can not build ideal devices the actual refrigerator will require more work than the power plant will produce extra.