Question 539: Thermodynamics & KTG

Question

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$$^\circ$$C to 70$$^\circ$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min
$$-$$1
.
[Heat of combustion = 8 $$	imes$$ 10
3
Jg
$$-$$1
, Specific heat of water = 4.2 Jg
$$-$$1
$$^\circ$$C
$$-$$1
]

Accepted Answer

$$Q = ms\Delta T$$
$${{dQ} \over {dt}} = {\left( {{{dm} \over {dt}}} ight)_{water}}S\Delta T = {\left( {{{dm} \over {dt}}} ight)_{oil}}C$$
$$ \Rightarrow 2 	imes 4.2 	imes {10^3} 	imes 40 = {\left( {{{dm} \over {dt}}} ight)_{oil}} 	imes 8 	imes {10^6}$$
$$ \Rightarrow {\left( {{{dm} \over {dt}}} ight)_{oil}} = {{8 	imes 4.2 	imes {{10}^4}} \over {8 	imes {{10}^6}}}$$ kg/minute
= 42 g/min

Thermodynamics & KTG

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$^\circC to 70^\circC. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min -1 . [Heat of combustion = 8 \times 10 3 Jg -1 , Specific heat of water = 4.2 Jg -1 ^\circC -$1 ]

Integer / Numeric Answer Type