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A geyser heats water flowing at the rate...

A geyser heats water flowing at the rate of 3.0 litres per minute from `27^@` C to `77^@`C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is `4.0xx10^4` J/g ?

Text Solution

Verified by Experts

Volume of water heated
V = 3 liter/min.
`=3xx10^(-3) m^3//"min".`
Density of water `rho=10^3 "kg m"^(-3)`
Mass of water heated `m=rhoV`
`=10^3 xx 3xx10^(-3)`
`= 3 "kg min"^(-1)`
Increase in temperature `Deltatheta =77-27=50^@`C
Specific heat of water `C=4.2xx10^(-3) "J kg"^(-1) .^@C^(-1)`
Amount of heat used for heating water,
`Q.=mCDeltaT`
`=3xx4.2xx10^(+3)xx50`
`=63xx10^4` J/min...(1)
Suppose, rate of combustion of fuel is m kg/min Heat corresponds decrease in rate of combustion,
`Q=mxx4xx10^7` J/min ...(2)
Heat is used for heating water of mass m = corresponds decrease in rate of combustion
`therefore 63xx10^4=mxx4xx10^7`
`therefore m=(63xx10^4)/(4xx10^7)`
`therefore m=15.75xx10^(-3)` kg/min
`therefore` m=15.75 g/min
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