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. The desity of natural gas is `0.740 g L^(-1) (1.013 xx 10^(5)Pa, 25^(@)C)` specified by PUC , the public utility company. (a) Calculate the amount of methane and ethane (in moles) in `1.00m^(3)` of natural gas (natural gas, methane and ethane are not ideal gases). (b) Calculate the combustion energy which is released as thermal energy during the buring of `1.00 m^(3)` of natural gas under standard conditions assuming that all products are gaseous .(if you do not have the amount from 1.2 a) assume that `1.00 m^(3)` natural gas corresponds to 40.00 mol natural gas) According to the PUC the combustion energy will be 9.981K Wh per `m^(3)` of natural gas if all products are gaseous . How large is the deviation (in percent) from the value you obtained in b? The swimming pool inside the house is 3.00 m wide ,5.00 m long and 1.50 m deep (below the floor) . The tap water temperature is `8.00^(@)C` and the air temperature in the house (dimensions given in the figure) is `10.0^(@)C.` Assuming a water density of `rho=1.00 Kg L^(-1)` and air behaving like an ideal gas.