Assume that for a domestic hot water supply `150 kg` water per day must be heated from `10^(@)C` to `65^(@)C` and gaseous fuel propane `C_(3)H_(8)` is used for this purpose. What moles and volume of propane (in `L` at `STP)` would have to be used for heating domestic water, `DeltaH` for combustion of propane is `-2050kJ mol^(-1)` and specific heat of water is `4.184 xx 10^(-3) kJ g^(-1)`.

Answer

`3.77 xx 10^(2)` litre

Explanation

Heat taken up by water `= mS ? T`
`=150 xx 1000 xx 4.184 xx 10^(-3) xx 55 = 34518 kJ`
`:.` 2050 kJ heat is provided by 1 mole `C_(3)H_(8)`
`:.` 34518 kJ heat is provided by `= 34518//2050`
`= 16.83` mole `C_(3)H_(8)`
`:.` Volume of `C_(3)H_(8)` at NTP `= 16.83 xx 22.4` litre
`= 3.77 xx 10^(2)` litre