Can someone help with this?

Useful Formulae and Numbers Radius of Earth: 6.4x10m Energy flux from Sun above atmosphere= 1370 W m2 ke=Boltzmann's constant=1.38x10-23 J K1 Latitude of Philadelphia: 40 degrees N o=Stefan-Boltzmann constant=5.67x10-8 Jsm2K Population of USA: 3x108 g = 9.8 ms? Population of world: 7x109 Energy units: 1J = 1 kg m? s? Mass: 1 kg = 2.2 lb 1 Btu = 1055 J 1 metric ton=1000 kg (I will use this as "1 ton") 1 cal = 4.184 J Power: 1 Watt = 1 W = 1 J st 1 Cal = 1 kcal = 4184 J (food) Length: 1 foot = 0.305 m; 1 mile = 1609 m 1 kWh = 3.6x10j (Temp in K) = (Temp in C)+273 = (Temp in F)*5/9+255 1 quad = 1015 Btu = 1.055x1018 J = 1.055 EJ Fuel CO2 emitted Energy content Energy content (MJ/kg) (kg/GJ) Wholesale cost Retail cost Coal (avg) 25 GJ/ton 25 88 $50/ton Crude Oil 6.12 GJ/bbl 43 71 $94/bbl Gasoline 0.13 GJ/gal 47 67 $3.80/gal Natural Gas 1.08 GJ/kcf 55 51 $4.00/kcf $10/kcf Electricity $0.04/kWh $0.12/kWh (9) I have the choice of heating my house by burning natural gas or by running a heat pump using electricity. (a) What coefficient of performance (COP) does the heat pump need to have to be cheaper to operate than the gas furnace? (Assume the furnace is 90% efficient, use the fuel costs shown on the first page of the exam, assume that the purchase price of the heater is the same in the two cases, and this is being used in Philadelphia weather). (b) What COP does the heat pump need in order to have a lower total CO2 output than the gas furnace? Assume the electricity is being made from a coal power plant that operates at 35% efficiency. (c) Is it physically possible to build a heat pump with the coefficient of performance you need for parts (a) and (b)