Question

For his 18th birthday in February Peter plants to turn a hut in the garden of his parents into a swimming pool with an artifical beach. In order to estimate the consts for heating the water and the house , peter obtains the data for the natural gas combustion and its price.
Calculate the energy (in MJ) which is needed to maintain the temperature inside the house at `30.0^(@)C` during the party (12 hours) .
`1.00 m^(3)` of natural gas as delivered by PUC costs 0.40 € and `1.00 k` Wh of electricity costs 0.137 € . The rent for the equipment for gas heating will cost him about 150.00 € while the corresponding electrical heaters will only cost 100.00 €.

Answer 1

Correct Answer - Energy for maintaining the temperatue:
Surface area of the house:
Ahouse `=3m xx46 m + 8m xx 2m + ((2m)^(2)) + (4m)^(2))^(1//2) xx 2xx 15m=288.16 m^(2)`
`Heat conductivity : `lambda_("wall") =1J (s KM)^(-1)`
Energy flux along a temperature gradient (wall thickness d=0.2 m)
`J=Eloss (Axx Deltat)^(-1) = lambda_("wall") DeltaT d^(-1)`
`E_("loss") = 288.16 m^(2) xx (12.60.60s) xx 1 J (s km)^(-1) xx 25 K xx (0.2m) ^(-1) =1556 MJ`
`E_("loss") =1556 MJ`