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Answer: 1026s, 17.1m
Explanation:
Given
COP of heat pump = 3.15
Mass of air, m = 1500kg
Initial temperature, T1 = 7°C
Final temperature, T2 = 22°C
Power of the heat pump, W = 5kW
The amount of heat needed to increase temperature in the house,
Q = mcΔT
Q = 1500 * 0.718 * (22 - 7)
Q = 1077 * 15
Q = 16155
Rate at which heat is supplied to the house is
Q' = COP * W
Q' = 3.15 * 5
Q' = 15.75
Time required to raise the temperature is
Δt = Q/Q'
Δt = 16155 / 15.75
Δt = 1025.7 s
Δt ~ 1026 s
Δt ~ 17.1 min
The non-relativistic formula for low speed v < 0.1c is:
K.E = 0.5mv^2 = 0.5 * 235 * (7)^2 = 5757.5 J
C i would think
it sounds best