MATH SOLVE

3 months ago

Q:
# Assume that you heat your home with a heat pump whose heat exchanger is at Tc=2βC, and which maintains the baseboard radiators at Th=47βC. If it would cost $1000 to heat the house for one winter with ideal electric heaters (which have a coefficient of performance of 1), how much would it cost if the actual coefficient of performance of the heat pump were 75% of that allowed by thermodynamics?

Accepted Solution

A:

Answer:$187.61 Step-by-step explanation:Data provided:Temperature of the heat exchanger, Tc = 2Β° C = 273 + 2 = 275 KTemperature of the base board radiators , Th=47Β° C = 273 + 47 = 320 KCost of heating the house = $1000Coefficient of performance of the heat pump = 75% = 0.75Now,Actual performance = 75% of performance of heat pumporActual performance = 0.75 Γ [tex]\frac{\textup{Th}}{\textup{Th-Tc}}[/tex]
orActual performance = 0.75 Γ [tex]\frac{320 K}{320-275}[/tex]
orActual performance = 0.75 Γ [tex]\frac{320}{45}[/tex]
orActual performance = 5.33 Therefore, the cost = [tex]\frac{\textup{1000}}{\textup{5.33}}[/tex]
orcost = $187.61