A gaeyser heats water flowing at the rate of 3 kg per minute from `27^(@)C` to `77^(@)C` . If the geyser operates on a gas burner, what is the rate of consumption of fuel if the heat of combusion is `4 xx 10^(4) J//g?` Given specific heat of water is `4.2 xx 10^(3) J//kg//K`.

Explanation

Here, `m= 3 kg//mi n`,
`Delta T = 77 - 27 = 50^(@)C = 50 K`
heat sphent to raise the temperature `Delta T` of water is `Q = mc Delta T`
` = 3 kg//mi n xx (4.2 xx 10^(3)) Jkg^(-1) K^(-1) xx 50 K`
`= 63 xx 10^(4) J//mi n`
Rate of consumption of fuel
`=(Q)/("heat of compustionof fuel")`
`=(63 xx 10^(4) J//mi n)/(4 xx 10^(4) Jg^(-1))` `= 15.75 g mi n^(-1)`.