I have read that heat pumps are more efficient than generating heat directly for heating homes, until the temperature gets down to a critical value.
I just asked how to calculate temperature of gasses: Behavior of gasses, ideal and otherwise
and have a little octave code
function T2 = compressedgas(cp, cv, P1, V1, T1, P2) gamma = cp/cv; % approx 7/5 for dry air R = 8.3; V2 = V1 * ( P1/P2)^(1/gamma) n = P1 * V1 / (R * T1); T2 = P2 * V2 / (n * R); end
For air at STP, T = 298, P = 102kPa, compressed to P2 = 714kPa, I get a temperature of 1005 K given gamma = 1.4
Assuming a pressurized tank allowed to radiate heat until it cooled down, this seems like a very efficient heat source indeed.
When I change the assumption to very cold air T = 248 the temperature is still 839K.
This seems hot enough that I don't understand why heat pumps should ever be less efficient than directly heating the house, so can anyone identify the engineering details that make this difficult?